Expired H1B petition transfer to new employer

My H1B petition was approved with Indian employer in 2016. I stayed in USA from Jul 2017 till Dec 2020 and returned to India in JAN 2020.

At the time of returning to India my H1b extension petition was approved from 2019 till March-2022.

In Aug-2021 I changed my employer and again in Nov-2022 while I was in India only.

Can my new employer(3rd) file my H1B petition in cap-exempt now and I will get a chance to utilize my remaining 3 year out of total 6 years of H1B ?

Yes, you can use any remaining time not used against the 6 year term including any time you spend outside of the US when being on H1B status for e.g. vacation time spent in India while you were employed in the US on H1B. The H1B will be cap-exempt.

Thank you for a reply ! Can I apply for Cap-Exempt H1B only once in a year(April-May) or through out the year ?

Cap-exempt can be applied any time.