Running a scheduled job every 1 minute and 15 miutes.

1) 1 Minute logic:

i)
ClassName cls = New ClassName();
            String myDateTime = String.Valueof(datetime.now().addseconds(10));

            String[] strs =myDateTime.split('-',5);  

            String[] strs2=strs[2].split(':',5);

            String[] strs3=strs2[0].split(' ',3);

            String schdul= strs2[2]+' '+strs2[1]+' '+strs3[1]+' '+strs3[0]+' '+strs[1]+' '+'?';  
           
            system.schedule('jobid',cls,wfbatch);
ii)
          ClassName cls = New ClassName();

            Datetime dt = DateTime.now();
            Integer nextMinute = dt.minute() + 1;
            if (nextMinute > 59) {
                nextMinute -= 60;
            }
            String scheduleString = '1 ' + nextMinute + ' * * * ? *';
            system.debug('-------'+scheduleString);

system.schedule('jobid',cls,wfbatch);

2) 15 Minute logic:

System.schedule('Scheduled Job 1', '0 0 * * * ?', new ScheduledClass());
System.schedule('Scheduled Job 2', '0 15 * * * ?', new ScheduledClass());
System.schedule('Scheduled Job 3', '0 30 * * * ?', new ScheduledClass());
System.schedule('Scheduled Job 4', '0 45 * * * ?', new ScheduledClass());

Note:

global class Scheduler02 implements Schedulable {

    global void execute(SchedulableContext SC){
        //Call other class method which will perform operations as it is 
        //recommended that all processing take place in a separate class
        doScheduling();
    }
    public void doScheduling(){
      try{
            dateTime dt=System.now().addMinutes(10);
            String Csec,Cmin,Chr,Cday,Cmonth,CYear;
            Csec=String.valueof(dt.second());
            Cmin=String.valueof(dt.minute());
            Chr=String.valueof(dt.hour());
            Cday=String.valueof(dt.day());
            Cmonth=String.valueof(dt.month());
            CYear=String.valueof(dt.Year());
            String SchTimer=Csec+' '+Cmin+' '+Chr+' '+Cday+' '+Cmonth+' ? '+CYear;
            system.debug('*************SchTimer:'+SchTimer);
            Scheduler01 cas = new Scheduler01();
            system.schedule('Scheduler01: Running at '+System.now().format(), SchTimer, cas);
            //we will delete completed apex scheduled jobs for which state is DELETED
            for( CronTrigger c:[Select State,Id,EndTime,CronExpression From CronTrigger  
                                where NextFireTime=null  AND State='DELETED' Limit 100]){
                    System.abortJob(c.id);
            }
        }
        catch(exception e){
        }
    }
}