Third payment mode is not clear form your question:-

1. Is it cash payment on 20-7-2020 ?
2. is it a account transfer from the bank account of son of purchaser. if it is account transfer then it is through net banking or other mode.  Please clarify your question. or?
3. is it cash payment by son of purchaser. ?

We will analyse applicability of section 269ST in each case.
As per section 269ST, no person shall received an amount of Rs. 200000/- or more in any mode otherwise than account payee cheque/draft or electronically clearing system (BHIM, UPI, Net banking) :- In aggregate from a person in a day.or in respect of a single transaction. or In respect of transactions relating to single event or occasion from a person.  
But this is not applicable on any receipts of :-
Government
Banking company
Post office saving bank and Co-operative bank.

coming to your question, Purchase of car is a single transaction. Hence if cash payment (on same day or different days) in relation to this single transaction is equal to or  more than rs. 200000/- Then section 269ST shall apply and for voilation of this section the receiver will be liable to a penalty of an amount equivalent to the amount of transaction.
 
the first payment is through bank, then we assume that it is though account payee cheque, draft or net banking mode etc. Hence there is no voilation of section 269ST.
The second payment is Rs. 150000/- is in cash. But is it below limit specified in section 269ST.
The third payment. 

• if third payment is cash payment being rs. 150000/- then total cash payment in relation to single transaction i.e. car sale becomes Rs. 300000/- which is more than limit specified in section 269ST. Hence receiver is liable to penalty. Even if this payment is made in cash by the son of purchaser and not the purchaser itself. Still receiver is liable to penalty because this payment is in relation to a single transaction i.e sale of car. 
• If third payment is transferred to account though net banking or other mode then section 269St not applicable and total cash payment in relation to car purchase remains below Rs. 200000/- hence no penalty. If account transfer payment is done by son of purchaser, still if it is not a cash payment hence sec. 269st is not applicable.
• The treatment of the payment done by son for this father, depends on the arrangement between the two. if this money will be returned by father to son then it may be treated as unsecured family loan. Or if this money is non-returnable then it may be treated as gift.