If USCIS has rejected the h1b petition , can we send back after the filing date

Let’s say USCIS has rejected a h1b petition ( i129 ) due to incomplete form or some other administrative error then can we follow up and resubmit that after June ?

When you say June, do you mean after your current I-94 is expired? If yes, you need to work with your attorney to check if you can be eligible for NPT filing.

Sorry April 1 H1b lottery selects get 3 months to submit their petition successfully. so 3 months from Apr 1st is June 30