If your son has a Singapore citizenship, though he has been in India since LKG, he will be considered as a Foreign National. Civilians in India do not usually get dual citizenship and so he cannot be considered an Indian Citizen. Having said that, your son is eligible for NEET if he fulfils the eligibility critera which is mentioned here. And if your son gets a seat in MBBS, he can study in India.

NEET 2020 ELIGIBILITY CRITERIA:

• Indian Nationals, NRIs, PIOs, OCIs, and Foreign Nationals
• No upper age limit as of now. The Candidate should be at least 17 years by December 31st of 2020
• You should have completed your 10+2 with Physics, Chemistry and Biology as your Core Subjects.
• 50% Aggregate in Physics, Chemistry and Biology for General Category, 45% for PWD and 40% for OBC,SC,ST Candidates.
• NIOS and Private Candidates are also eligible