Part Time Position at School with H1b Visa from Current Employer

I have H1B with my full time employer. PERM/I-140 approved. Waiting for priority date to become current to move forward with green card process. I'm going to grad school at night. Can I accept a Teaching Assistant position at the same school where I am doing my grad studies? This position will not require half day of work... Probably 1 hour per day or so. Will this create issues with my current imigration processes? It is paid small fee...

Any work with an additional employer requires work authorization. Illegal work is a serious problem for any immigration processing. Do not do it.

It is doubtful that the school would file an H-1B petition for a TA/RA. These are generally more than a 1 hour per day time commitments as well. Have you been totally honest with the school about your immigration status? I suspect you have not, because no one I know at a university would make this time of offer for 5 hours a week of work from a TA/RA.