To maintain variable value inside the Salesforce Batch class, Database.Stateful can be used.

Sample Class:

global class Class_Name implements Database.Batchable<sobject>, Database.Stateful {
    
    Integer i = 0;
    
    global Database.QueryLocator start( Database.BatchableContext bc ) {
        
        return Database.getQueryLocator(
            'SELECT Id, Name FROM Account'
        );
        
    }
    
    global void execute( 
        Database.BatchableContext bc, 
        List < Account > listAccounts 
    ) {
        
        for ( Account objAccount : listAccounts ) {
            
            i += 1;
            
        }
        
    }
    
    global void finish( Database.BatchableContext bc ){
    }
    
}

here i value will be maintained even though execute method is called several times.