will a part time job to make extra money effect my MBA application?
It shouldn't, but who knows. If your employer is a corporation, you could probably list them as your employer and that you are part time while you study. Say that the company is a steakhouse. I doubt that they expect more than that. 

But, it is a good thing that you want to concentrate on studying up in preparation for the MBA, so stress that more than the specific job description. 

Some would just ignore it. Some would get a chuckle. Others ..., well, there are lots of sorts of people in the world. 

Just make your application show the strength of your background and the likelihood of future success. That is what they will be looking for.