Batch apex to update ID with no duplicate phone and account

I am creating a batch for the requirement in which if contact has duplicates based on account and mobile phone than field named Eksternal ID should not set the value. Can anyone guide me with this requirement? Thanks in advance

This is my code now, but it still not right, cause eksternal ID with duplicate contact still can set the value.

public class UT_MDM_batchEksternalIDContacts implements Database.Batchable <sObject>,Database.Stateful {   
    final Integer MAX_TEXT_LENGTH = 255;
    public  UT_MDM_batchEksternalIDContacts(){
    }

    public  Database.QueryLocator start(Database.BatchableContext info){  
        String SOQL = '';
        if(Test.isRunningTest()){
            SOQL = 'SELECT Id,Eksternal_ID__c,AccountId, Account.SAP_Account_Id__c, LastName, Title, MobilePhone FROM Contact WHERE MobilePhone != null AND LastName != null AND Account.SAP_Account_Id__c != null AND Title != null AND Is_Drop__c = FALSE';
        }else{
            SOQL = 'SELECT Id,Eksternal_ID__c,AccountId, Account.SAP_Account_Id__c, LastName, Title, MobilePhone FROM Contact WHERE Eksternal_ID__c = null AND MobilePhone != null AND LastName != null AND Account.SAP_Account_Id__c != null AND Title != null AND Is_Drop__c = FALSE LIMIT 100';
        }

        return Database.getQueryLocator(SOQL);
        
    }     
 
    public void execute(Database.BatchableContext info, List<Contact> listContact){
        Set<Id> S_ContactIds = new Set<Id>();
        List <String> S_Lastname = new List<String>(); 
        List <String> S_Phone = new List<String>();
        List <String> S_Account = new List<String>();
        List <String> S_Title = new List<String>();
        
        Integer tempUpdate;
        for(Contact cont : listContact){
            if(cont.MobilePhone != null && cont.LastName != null && cont.AccountId != null && cont.Title != null ){
                S_ContactIds.add(cont.Id); 
                S_Lastname.add(cont.LastName);
                S_Phone.add(cont.MobilePhone);
                S_Account.add(cont.AccountId);
                S_Title.add(cont.Title);
            }
        }
        List<Contact> contractorList = [SELECT Id, MobilePhone,AccountId FROM Contact WHERE MobilePhone =:S_Phone AND AccountId =:S_Account AND ID NOT IN :S_ContactIds]; //duplicate
        List<Id> contIds = new List<Id>();
        if(S_ContactIds.size() > 0){
           if(contractorList.size() > 0 ){
                for(Contact contactVal : listContact){ 
                    for(Contact contList: contractorList){ 
                        if(contactVal.MobilePhone == contList.MobilePhone && contactVal.AccountId == contList.AccountId){//error
                        }
                        else{
                            contIds.add(contList.Id);
                        }   
                    }            
                }     
            }
            List<Contact> finalList = new List<Contact> ([SELECT Id, Eksternal_ID__c, Account.SAP_Account_Id__c, LastName, Title, MobilePhone FROM Contact WHERE Id IN :contIds]); //
            if (contIds.size() > 0){
                updateContact(finalList);
            }
            else if (contractorList.size() == 0 ){
                updateContact(listContact);
            }
        }
    }
   
    public void updateContact(List<Contact> listContact) {
        List<Contact> lstContact = new List<Contact>();
        List<Id> accountIds = new List<ID>();
            for(Contact cont : listContact){
                accountIds.add(cont.AccountId);
            }
            Map<Id,Account> accountMap = new Map<Id,Account>([SELECT ID,SAP_Account_Id__c FROM ACCOUNT
                                                              WHERE ID IN:accountIds]);
            Account tempAccount = null;
            for(Contact cont : listContact){
                if(accountMap.containsKey(cont.AccountId)){
                    String mobile = cont.MobilePhone.replaceAll('\\D','');
                    tempAccount = accountMap.get(cont.AccountId);
                    if(tempAccount.SAP_Account_Id__c != null){
                        cont.Eksternal_ID__c =  cont.LastName + '_' + tempAccount.SAP_Account_Id__c + '_'+ cont.Title + '_'  + mobile  ;
                        // Ensure that the search text does not exceed max length:
                        cont.Eksternal_ID__c = cont.Eksternal_ID__c.left(MAX_TEXT_LENGTH);
                        lstContact.add(cont);
                    }
                }
            }
            update lstContact; 
    }
    
   public void finish(Database.BatchableContext info){ 
       
   } 
}