-Yes, you can apply for part-time H1 to get the H1 status if your salary is low. Usually, part-time job means working hours/week is between 20 and 34. You can also file a h1 amendment to change your part-time H1 to full time H1 if your salary increase to the full time level later. Or if you find a full-time job, you can do the H1 transfer to the new employer to get the full-time H1 status.
Anyway, Part-time H1 status is equal to full-time H status, so your status is H1 status no matter whether you work for part-time job or full time job.