Perm filed outside 365 days. H1b extension filed til max out date

Perm filed outside 365 days. Now approved.
Last extn filed - aug 2020
Extn approved - june 7 2021
Approved until - jun 9 2021, while filing extension forgot to add that i had perm approved so got approved only till h1b max out date.
Current petition i-94 expires june 19 2021.

Am in usa still as my company is looking into my case. Do you think my attorney can file a NPT.( due to the earlier miss, covid situation and a baby who is a us citien) what would be my best option in this case.

It depends on the case details. Its not clear that why your employer missed filing extension.

Human error. Attorney missed out on the details. What can be my best option?

NPT can be filed. The approval chances will depend on officer who works on your case.