How to update error message back to processed record in Salesforce batch apex?

Can anyone guilde me how to update the error message back to the processed record in salesforce if any error occurs in batch apex.

I am processing records from SIS_Staging__c object to create or update contact based on condition, if any error occurs for any record then I want to update the error field on SIS_Staging__c object.

Below is my code of batch apex where I used database.savepoint method to rollback the changes if any error occurs.

can anyone guide me on this, I don’t have any idea how to process error message back to processed record please.

global class newbatchapex implements Database.Batchable<sObject>, 	Database.stateful{
    global Database.QueryLocator start(Database.BatchableContext BC) {
        return DataBase.getQueryLocator([SELECT Id,Name,Status__c,SIS_Student_ID__c ,First_Name__c,Last_Name__c,Email__c,Mailing_Country__c,SIS_Application_Id__c,AdmTyp__c,Resident_Tuition__c,ActnRsn__c,Admit_Term__c,Home_Country__c,Plan__c,Prog1__c,Prog__c,
                                          ProgActn__c
                                         FROM SIS_Staging__c
                                        ]);
    }
    global void execute(Database.BatchableContext BC , List <SIS_Staging__c> staginglist) {
		Set<String> uniquekeySet = new Set<String>();
		for(SIS_Staging__c stagingObj : staginglist){
			uniquekeySet.add(stagingObj.SIS_Student_ID__c);
		}
		List<Contact> contactToUpdate = new List<Contact>();
		List<Contact> contactToInsert = new List<Contact>();
		Map<String,Contact> studentIdTOContact = new Map<String,Contact>();
        Savepoint sp = Database.setSavepoint();
		List<Contact> conList2 = [SELECT ID,SIS_Student_ID__c,FirstName,LastName FROM CONTACT WHERE SIS_Student_ID__c IN:uniquekeySet];
		for(Contact conObj : conList2){
			studentIdTOContact.put(conObj.SIS_Student_ID__c,conObj);	
		}
        for (SIS_Staging__c acct : staginglist){ 
              if(studentIdTOContact.containsKey(acct.SIS_Student_ID__c)){
				 Contact con = studentIdTOContact.get(acct.SIS_Student_ID__c);
				 con.FirstName = acct.First_Name__c;
                 con.LastName = acct.Last_Name__c;
                 con.hed__AlternateEmail__c = acct.Email__c;
                 con.SIS_Student_ID__c = acct.SIS_Student_ID__c;
                 con.hed__Country_of_Origin__c = acct.Home_Country__c;
                 con.Current_Country_of_Study__c = acct.Mailing_Country__c;
                 con.SIS_Application_Id__c = acct.SIS_Application_Id__c;
				 contactToUpdate.add(con);

			  }else{
				  Contact con = new Contact();
				 con.FirstName = acct.First_Name__c;
                 con.LastName = acct.Last_Name__c;
                 con.hed__AlternateEmail__c = acct.Email__c;
                 con.SIS_Student_ID__c = acct.SIS_Student_ID__c;
                 con.hed__Country_of_Origin__c = acct.Home_Country__c;
                 con.Current_Country_of_Study__c = acct.Mailing_Country__c;
                 con.SIS_Application_Id__c = acct.SIS_Application_Id__c;
                 con.LeadSource = acct.Status__c;
                 contactToUpdate.add(con);
				  
			  }
        }
        try{
            //insert contactToInsert;
            upsert contactToUpdate;
        }
        catch(exception e){
            string s = 'Error: ' + e.getMessage();
            database.rollback(sp);
        }