Have the supplementary agreement vetted by a competent lawyer, first. If there are any clauses detrimental to your interests, ask for suitable amendments. If the builder refuses to accommodate your request, do not sign. Lodge a written complaint with the State RERA authority. Issue a legal notice and complain to the consumer forum as well.

Refuse to sign the suplementary agreement 

if builder refuses to deliver possession file complaint against builder before RERA and seek orders to direct builder to deliver possession 

Builder cannot deviate from main agreement. He has to put the agreement holder in possession before the date stipulated without seeking any further agreement of amendments to main agreement. You can approach RERA Authority or District Consumer Commission against builder under new Consumer Protection Act, 2019. Proceeding in District Consumer Commission under new Act are very fast, District Consumer Commission have power to grant interim relief and order arrest of builder. Issue lawyer's notice  seeking compliance of agreement and after the file a complaint in District Consumer Commission. Order will be issued  by District Consumer Commission to builder to enforce the terms of agreement, you will be entitled to payment of rent during the proceeding, you will get compensation  for mental harassment, cost of complaint and lawyer’s fee.

You can strongly object to the supplementary agreement which would be against your interests. 

If in case you are helpless to take possession then you may sign the same with objection and can file a suit subsequent to taking possession to declare the supplementary agreement as null and void since it was obtained by force or coercion.

if the supplementary agreement does not modify the carpet area to be allotted to you and the amenities and services promised to you [basis which you agreed to purchase the flat] as agreed in the original agreement, then i dont think there would be any problem in signing the supplementary agreement

however the manner in which he has required you to sign the supplementary agreement is outright illegal and it is like holding someone to ransom or blackmailing 

however in order to avoid any controversy you can sign on the supp agreement if you are entitlements as originally agreed are not materially changed or modified in the supp agreement 

No it's illegal. For supplementary agreement consent of majority in writing is needed 

1. No agreement can be forceful, so is the case with the supplementary agreement. If you don't agree with it, don't give in to the threats. 
2. You can and must lodge a police complaint against him for the threats of violence. 
3. He isn't legally entitled to prevent possession. If he does so, you have to move the consumer court. 
4. You obviously need legal assistance for 4. I extend my expert legal services to you. You have to visit my office for further consultation. 
5. ९८२०८९७८८४ (Nine eight two zero eight nine seven eight eight four) 

Dear client I am sorry to hear that but in this case you may go through the agreement and see whether it is harmful to you or not if in case it is not harmful you must sign the agreement or if it is harmful then you must consult a lawyer for the same

- If there is already sale agreement after mentioning the details of terms and conditions , then it cannot be rectified or changed without getting your consent 

- Hence, the builder cannot threaten you for stopping the possession , and if it done then you can take legal action against him .

- You can file a compliant against him before the Consumer forum for getting relief .