There is no OOTB where it captures the log for scheduled job whether it ran or not.
You can do 1 thing over here, take the script written in scheduled job & execute it in background scripts to check if there is any error. You can add some manual logs to it by adding gs.info at different places/lines to check till which line or executes. This way u should come to know whether there is any error which u need to address or not.
You can also refer this link where they are asking to do the same.
