Please find the test class of your code.

Please make the index public so that you can assign value in the test class.

public integer index = 0;

global class Diplayaccrelatecon {
    
    private integer totalRecs = 0;      
    public integer index = 0;
    private integer blockSize = 5;
   
   // public boolean prev {get; set;}
    //public boolean nxt {get;set;}
    //public boolean frt {get;set;}
    //public boolean sec{get;set;}
   
    //public List<Account> accList{get;set;}
   public list<Contact> conList{get;set;}
   public String accId{get;set;}
   
  public Diplayaccrelatecon () {
              totalRecs = [select count() from Account];    

     }        
    public List<Account> getacc() {//get will take the value from apex to vf
        List<Account> accs = Database.Query('SELECT id,name,phone FROM Account LIMIT :blockSize');//queried dynamically as string
        System.debug('Values are ' +accs);
        return accs;
    }          
    public void first() {
        index = index - blockSize;
        getacc();
    }     
    public void second() {
        index = index + blockSize;
       getacc();
    }
    public void save(){
        update conList;
    }
    public boolean getdisablefrt() {
        if(index == 0)
            return true;
        else
            return false;
    }      
    public boolean getdisablesec() {
        if((index + blockSize) > totalRecs)
        return true;
        else
        return false;
    }       
       public PageReference dispalyContact() {
       system.debug('accId'+accId);        
         if(accId != null) 
             System.debug('Index Inside display Contact:::'+index);
         if(index>=0)      
  {
      System.debug('inside dispalyContact index:::::'+index);
      System.debug('inside dispalyContact blockSize:::::'+blockSize);
      conList=[SELECT id,Name,FirstName,LastName,email FROM Contact where AccountId=:accId   LIMIT :blockSize];
  }          system.debug('conList::::::::::::::::::::::'+conList);   
             return null;       
 }     
        
    public void previous() {
        index = blockSize - index;
        dispalyContact();
    }     
    public void next() {
        index = index + blockSize;
         dispalyContact();
    }            
             
    public boolean getdisableprev() {
        if(index == 0)
            return true;
        else
            return false;
    }       
    public boolean getdisablenxt() {
        if((index + blockSize) > totalRecs)
        return true;
        else
        return false;
    }     

     
}

@isTest
public class DisplayaccrelTestclass {
    
    @isTest
    static void call(){
        integer totalRecs = 0;     
        integer index = 0;
        integer blockSize = 5;    
        Account a=new Account();
        a.name='testacc';
        a.phone='testphone';
        insert a;
        contact c=new contact();
        c.firstName='testfirstName';
        c.LastName='testLastName';
        c.Email='test@gmail.com';
        c.AccountId=a.id;
        insert c;
        system.debug('1:'+c);
        
        Test.startTest();
        
        Diplayaccrelatecon d = new Diplayaccrelatecon();
        d.index=20;
        d.first();
        d.second();
        
        d.getdisablefrt();
        d.getdisablesec();
        d.next();
        d.previous();
        
        
        d.getacc();    
        c.AccountId=a.id;
        system.debug('2:'+a.id);
        contact con=[select id,Accountid from contact];
        
        system.assertEquals(con.Accountid, a.id);
        d.accId=a.id;
        d.dispalyContact();
        d.save();
        // d.getdisableprev();
        d.getdisablenxt();
        Test.stopTest();
    }
    @isTest 
    static void show(){
        integer totalRecs = 15;     
        integer index = 1;
        integer blockSize = 5; 
        Test.startTest();
        Diplayaccrelatecon ds=new Diplayaccrelatecon();
        //system.assertEquals(false, ds.getdisablefrt());
        ds.getdisablefrt();
        //system.assertEquals(false, ds.getdisablesec());
        ds.index=30;
        ds.getdisablesec();
        ds.getdisableprev();
        ds.getdisablenxt();
        Test.stopTest();
    }
}

Please let me know it is working or not??

Please mark it as the Best Answer if it helps you.

Thank You