-Your filing timing is OK. So, your status has no gap at all.
但是我今天跟學校的人打電話的時候發現各問題。我的offer是49%的工作量,也就是每周工作19.7小時。像我這種情況差一點點不到20小時/week,申請H1B會有問題嗎?
-Usually, Part-time H1 holder should work at least 20 hours/week to maintain his/her H1 status, but I hope USCIS is not so picky in your case and you still have a good chance to get it approved. It is strange to me why your school Human Resources did that to you? Did they hire a lawyer to deal with your case? You need to talk to HR or your professor seriously because USCIS may request RFE to ask your school to increase your working hours so that they can approve your part-time H1. You also need to keep a photocopy of the petition materials on your personal file so that you can find the problem.
By the way, I can feel this school is not good to you at all, so you have to continue your job search.