Apex class:
global class AhHandlingEmailservice implements Messaging.InboundEmailHandler {
    global Messaging.Inboundemailresult handleInboundEmail(Messaging.InboundEmail email, Messaging.InboundEnvelope envelope) {
        Messaging.InboundEmailResult result = new Messaging.InboundEmailresult();
        List<DY_Proposal_Attachment__c> proposalList = new List<DY_Proposal_Attachment__c>();
        List<Attachment> attList = new List<Attachment>();
        List<Error_Log__c> errorlogList=new List<Error_Log__c>();
        Map<String,Blob> AttachmentBody = new Map<String,Blob>();
        Set<Integer> proposalIdSet = new Set<Integer>();
        List<Integer> ProposalidsList=new List<Integer>();
        Map<Integer,String> Messagemap= new Map<Integer,String>();
        List<Id> SuccessIdsList= new List<Id>();
           
        try
        {
            for(Messaging.Inboundemail.Binaryattachment bAttachment: email.binaryAttachments){
                string fileName=bAttachment.fileName;
                  if(fileName.lastindexOf('_')!=-1 && fileName.endswith('.pdf')) {
                    Integer propId= integer.valueof(fileName.substring(fileName.indexOf('_')+1,fileName.indexOf('.pdf')));
                      ProposalidsList.add(propId);
                 }
                                
                }
            
         List<DY_Proposal_Attachment__c> dyproposal= new List<DY_Proposal_Attachment__c>([Select id,name,ProposalPDFID__c From DY_Proposal_Attachment__c where ProposalPDFID__c IN:ProposalidsList]);
         
         for(DY_Proposal_Attachment__c dypa:dyproposal){
            Integer propId= integer.valueOf(dypa.ProposalPDFID__c);
              proposalIdSet.add(propId);
         }  
         for( Messaging.Inboundemail.Binaryattachment bAttachment: email.binaryAttachments){
                 string fileName=bAttachment.fileName;
                 Blob body=bAttachment.body;
                 String Message='';
                 Integer propId=integer.valueof(fileName.substring(fileName.indexof('_')+1,filename.indexof('.pdf')));
             if(fileName.lastindexOf('_')!=-1 && fileName.endswith('.pdf')) {  
                 String name = fileName.substring(0,fileName.indexOf('.pdf'));
             if(!proposalIdSet.contains(propId)){
                      DY_Proposal_Attachment__c dypa = new DY_Proposal_Attachment__c();
                      dypa.Name = name;
                      dypa.ProposalPDFID__c = propId;
                      AttachmentBody.put(dypa.Name,body);
                      proposalList.add(dypa);
                     }else{
                       Message='Duplicate Record can not Insert';
                       Messagemap.put(propId,Message);
                                   
                    }
                   
                   }else{
                        Message='File Name should be a proper format';
                        Messagemap.put(propId,Message);  
                   }
                   
                  }  
            
           if(proposalList.size()>0){
                insert proposalList;
               
            }
              
            if(proposalList.size()>0){
              
              for(DY_Proposal_Attachment__c proAtt:proposalList){
                     Attachment attachment = new Attachment();
                     attachment.ParentId = proAtt.Id;
                     attachment.Body = AttachmentBody.get(proAtt.name);
                     attachment.Name = proAtt.name +'.pdf';
                     attList.add(attachment);
              }
            }
            
            if(attList.size()>0){
                             
             Database.saveResult[] attRecs = Database.insert(attList,false);
             for(Database.SaveResult sr:attRecs){
             if (sr.isSuccess()) {
                 SuccessIdsList.add(sr.getId());
                
             }
            
              }
                   
                }
            
             if(SuccessIdsList.size() == email.binaryAttachments.size()){
                 result.message = 'Your record(s) Successfully Inserted';    
             }
             else{
                  String myCustomMsg = 'The following attachment(s) insertion got failed.';
                
                 for(Integer aProposalId : Messagemap.keySet()){
                     myCustomMsg += 'The Attachment with the ProposalId '+aProposalId+' insertion got failed due to '+Messagemap.get(aProposalId)+' \n';   
                 }
                 result.message = myCustomMsg;
             }  
            
         }catch(Exception e){
              result.success = False;
              System.debug('Exception: '+e.getMessage());
              result.message = 'Failed to insert an attachment. '+e.getMessage();
              createErrorRecord(e.getMessage());
         }
              return result;
                  
         }
      
      public static void createErrorRecord(string exceptionMessage){
              system.debug('---ErrorLog----');
             Error_Log__c newErrorRecord = new  Error_Log__c();
                 newErrorRecord.Your_comments__c = exceptionMessage;
                // newErrorRecord.Name = fileName.substring(0,fileName.indexOf('.pdf'));
                 newErrorRecord.Name =  'Email Services Error Insert';
                 newErrorRecord.Processed_date__c = system.now();
                 newErrorRecord.Status__c = 'New';
                 newErrorRecord.Source__c = 'CorSales-StopLoss';
                 newErrorRecord.Object__c = 'DY Proposal';
                 newErrorRecord.Error_Type__c = 'Email Services';
                 Database.insert(newErrorRecord,false);
   }
    
  }


Test class:

@isTest(SeeAllData=False)

 public class AhHandlingEmailserviceTest{
   private static testmethod void Emailattachmentinsert(){

// create DY proposal attachment record

    DY_Proposal_Attachment__c Dyatt= new DY_Proposal_Attachment__c();
         Dyatt.name='Sample_786';
         Dyatt.ProposalPDFID__c= 786;
         Dyatt.Proposal_attached_successfully__c=true;
         insert Dyatt;
 // DY_Proposal_Attachment__c dyp=[select id,name,ProposalPDFID__c From DY_Proposal_Attachment__c where ProposalPDFID__c=:Dyatt.Id];
     Messaging.InboundEmail email = new Messaging.InboundEmail();
     Messaging.InboundEnvelope env = new Messaging.InboundEnvelope();
   
        email.subject = 'Test Proposal';
        email.fromname = 'sudhakar';
        env.fromAddress = 'rcomext.com';
     Error_Log__c newErrorRecord = new  Error_Log__c();
                 newErrorRecord.Name = 'Email Services Error Insert';
                 newErrorRecord.Processed_date__c = system.now();
                 newErrorRecord.Status__c = 'New';
                 newErrorRecord.Source__c = 'CorSales-StopLoss';
                 newErrorRecord.Object__c = 'DY Proposal';
                 newErrorRecord.Error_Type__c = 'Email Services';
                 Database.insert(newErrorRecord,false);
      Messaging.Inboundemail.Binaryattachment attachment = new Messaging.Inboundemail.Binaryattachment();
                 attachment.Body = Blob.toPdf('Sample PDF Text');
                 attachment.fileName = 'Sample_786.pdf';
      
      email.binaryAttachments = new Messaging.Inboundemail.Binaryattachment[]{attachment};
      
          AhHandlingEmailservice emailHandler = new AhHandlingEmailservice();
      Test.startTest();
      Messaging.Inboundemailresult result = emailHandler.handleInboundEmail(email, env);
            system.assert(result.success,'InbountEmailResult returnd a Failure message');
      Test.stopTest();
}

}