Please modified code here. Please handle any typo error.

public class RestapiCallclass {

    public void saveCalloutResult(){
        string[] urllist = new List<String>();
        urllist.add('https://preview.test1.com/ifsservice/issuer/getIssueList');
        urllist.add('https://preview.test2.com/ifsservice/issuer/getIssueList');
        urllist.add('https://preview.test3.com/ifsservice/issuer/getIssueList');
        urllist.add('https://preview.test4.com/ifsservice/issuer/getIssueList');
        urllist.add('https://preview.test5.com/ifsservice/issuer/getIssueList');
        
        for( Integer i=0; i< urllist.size(); i++ ){
        saveCalloutResult(urllist[i]);
        }
        }
     
    public void saveCalloutResult(string url){
         // Instantiate a new http object
        Http h = new Http();
        HttpRequest req = new HttpRequest();
        req.setEndpoint(url);
        req.setMethod('GET');
        req.setHeader('Content-Type', 'application/json');
        req.setHeader('Accept','application/json');
         system.debug('### '+ req);    
        String username = 'username';
        String password = 'password';
        
        Blob headerValue= Blob.valueOf(username + ':' + password);
        String authorizationHeader = 'Basic ' + EncodingUtil.base64Encode(headerValue);
        req.setHeader('Authorization', authorizationHeader);
        
        system.debug('###req### '+ req);            
        HttpResponse res = h.send(req);
        system.debug('###res### '+ res);
        
        string response = res.getBody();
        system.debug('### '+ response);
               
        List<JsonParserDetail> responseDetails = JsonParserDetail.parse(response); 
        system.debug('### '+responseDetails);
        
        String query = 'Select Id,Bankdir_Name__c from Issuer__c';
        ProcessIssuerBatch processBatch = new ProcessIssuerBatch(query,responseDetails);
        Database.executeBatch(processBatch,2000);
    }

}


Batch code
----------------------------

global class ProcessIssuerBatch implements Database.Batchable<sObject> {
    global List<JsonParserDetail> responseDetails;
    global String query;
    
    global ProcessIssuerBatch(String query,List<JsonParserDetail> responseDetails){
        this.query = query;
        this.responseDetails=responseDetails;
    }
    
    global Database.QueryLocator start(Database.BatchableContext BC) {
        return Database.getQueryLocator(query);
    }
     
    global void execute(Database.BatchableContext BC, List<Issuer__c> issuerList) {
        
        // process each batch of records
        Set<String> bankNames = New Set<String>();
        List<Issuer__c> InsertedIssuers = New List<Issuer__c>();
        for(Issuer__c eachIssuer : issuerList)
        {        
            If(!string.isBlank(eachIssuer.Bankdir_Name__c)){
                bankNames.add(eachIssuer.Bankdir_Name__c);
            }
            
            
        }
        
        if(responseDetails.size() > 0){
            for(JsonParserDetail jpd : responseDetails){
                If(! bankNames.contains(jpd.issuerBankdirName)){
                    InsertedIssuers.add(getIssuer(jpd.issuername,jpd.issuerBankdirName,jpd.processorName,jpd.subProcessorName,jpd.siloName));
                }
            }
        }
        
        try{
            If(InsertedIssuers.size() >0){
                insert InsertedIssuers;
            }
        } catch(Exception e) {
            System.debug(e);
        }
         
    }   
     
    global void finish(Database.BatchableContext BC) {
            AsyncApexJob a = [SELECT Id, Status, NumberOfErrors, JobItemsProcessed,
            TotalJobItems, CreatedBy.Email
            FROM AsyncApexJob WHERE Id =
            :BC.getJobId()];
            
            // Send an email to the Apex job's submitter notifying of job completion.
            Messaging.SingleEmailMessage mail = new Messaging.SingleEmailMessage();
            String[] toAddresses = new String[] {a.CreatedBy.Email};
            mail.setToAddresses(toAddresses);
            mail.setSubject('ProcessIssuerBatch Completed ' + a.Status);
            mail.setPlainTextBody
            ('The batch Apex job processed ' + a.TotalJobItems +
            ' batches with '+ a.NumberOfErrors + ' failures.');
            Messaging.sendEmail(new Messaging.SingleEmailMessage[] { mail });
    }
  
   // -- utility method
   global Issuer__c getIssuer(string iName, string ibName, string pName, string spName,string siloName){
        Issuer__c issuer = New Issuer__c();
        issuer.Name = iName;
        issuer.Bankdir_Name__c = ibName;
        issuer.Processor_Name__c = pName;
        issuer.SubProcessor_Name__c = spName;
        issuer.Silo_Name__c = siloName;
        return issuer;
    }
}

Please mark it best if it helps you. Thanks.

Regards,
Pawan Kumar