Reapplying for H1B visa after 221g rejection

If H1B Visa is rejected after 221g review, how soon can i appy for a new one on own or with another employer?I have to reapply with USCIS?What are the steps to be taken to file before the cap ?

You can apply as soon as the cap opens. There is no wait time. Process is same as previous H-1 filing.

Also, if you have copy of your old H-1 petition, you can apply for cap-exempt H-1 petition as well. This can be applied outside of cap. The process is same as previous H-1 filing, but you need to submit copy of old approved petition as proof that you have already made through the cap.