Hi Pranav,

Please find the below code and and update according to senario,in this trigger i used custom object, you just need to replace the same with your desired object which you want to use 
Apex Trigger :

trigger CountChildForEachParent on Child__c (after insert, after update, after delete, after undelete)  
{
    HandlerForChildToCountRecords handler = new HandlerForChildToCountRecords ();
    handler.run();
}

Apex Class :

public class HandlerForChildToCountRecords 
{    
    public void run()
    {
        if(trigger.isInsert || trigger.isUpdate && trigger.isAfter)
        {   
            afterInsertMethod(trigger.new);
        }
        
        if(trigger.isDelete  && trigger.isAfter)
        {   
            afterDeleteMethod(trigger.new,trigger.old);
        }
        
        if(trigger.isUpdate && trigger.isAfter)
        {   
            afterUpdateMethod( trigger.new, trigger.OldMap);
        }
    }
    
    private void afterInsertMethod(list<child__c>triggerNew)
    {
        //commonMethod(triggerNew,null);
        set<id> setOfId  = new set<id>();           
        for(child__c objChildNew : triggerNew)
        {
            if(objChildNew.Parent_name__c != null)
            {
                setOfId.add(objChildNew.Parent_name__c);
                system.debug('*****setOfId'+setOfId);
            }
        }
        if(setOfId.size() > 0)
        {
            //calling commom method to perofrm the operation, so as to reduce the line of code
            commonMethod(setOfId);
        }
    }
    
    Public void afterUpdateMethod( list<sobject> triggerNew, map<id,sobject> triggerOldMap)
    {
        set<id> setOfId = new set<id>();    
        
        list<child__c> lstChild = (list<child__c>) triggerNew;
        map<id, child__c> mapChild = (map<id, child__c>) triggerOldMap;
        for(child__c childObj : lstChild)
        {
            if(childObj.Parent_name__c != null && mapChild.get(childObj.id).Parent_name__c != null && childObj.Parent_name__c != mapChild.get(childObj.id).Parent_name__c)
            {
                setOfId.add(childObj.Parent_name__c);
                setOfId.add(mapChild.get(childObj.id).Parent_name__c);
            }
        }
        
        if(setOfId.size() > 0)
        {
            //calling commom method to perofrm the operation, so as to reduce the line of code
            commonMethod(setOfId);
        }
    } 
    
    private void afterDeleteMethod(list<child__c>triggerNew,list<child__c>triggerOld)
    {
        set<id> setOfId = new set<id>();           
        for(child__c objChildNew : triggerOld)
        {
            if(objChildNew.Parent_name__c != null)
            {
                setOfId.add(objChildNew.Parent_name__c);
                system.debug('*****setOfId'+setOfId);
            }
        }
        if(setOfId.size() > 0)
        {
            //calling commom method to perofrm the operation, so as to reduce the line of code
            commonMethod(setOfId);
        }
    }
    
    //Common Method to perform insertion/updation/deletion to query records
    private void commonMethod(set<id> setOfId)
    {
        try
        {           
            list<Parent__c> lstOfParent = new list<Parent__c>([select id,name,ContactsCount__c ,(select id,name from Child__r)
                                                                                                         from 
                                                                                                        Parent__c 
                                                                                                    where id IN:setOfId]);
            system.debug('*****lstOfParent'+lstOfParent);
            for(Parent__c objPrnt : lstOfParent)
            {
                if(objPrnt.ContactsCount__c != objPrnt.Child__r.size())
                {
                    objPrnt.ContactsCount__c = objPrnt.Child__r.size();
                }
            }
            update lstOfParent;
        }
        
        catch(DmlException e)
        {
            system.debug('The following exception has occurred: ' + e.getMessage()); 
        }  
    }          
}

This trigger also work on deletion of record and reparitng the parent of child, in both cases it will the child count.
Hope this help!

Thanks
Pranav