As per the eligibility criteria, it is compulsory for the candidates to complete their mandatory 12 months rotatory internship on or before July 30, 2020 to be eligible for AIIMS PG 2020. As your internship is completing on July 4, 2020 so this makes you eligible for AIIMS PG 2020. But there are other criteria also, you need to fulfil those.

https://medicine.careers360.com/articles/aiims-pg-eligibility-criteria