Is there any order in which liability of a person shall be discharged or it can be appropriated as per the convenience of the tax payer

No, every taxable person shall discharge his tax and other dues in the following order:
(a) self-assessed tax, and other dues related to returns of previous tax periods; b) self-assessed tax, and other dues related to return of current tax period;
(c) any other amount payable under the Act or the rules made thereunder including the demand determined under section 66 or 67.
Note 1:“tax dues” means the tax payable under this Act and does not include interest, fee and penalty.
Note 2:“other dues” means interest, penalty, fee or any other amount payable under the Act or the rules made there under.

(ICAI FAQ PUBLICATIONS 06-09-2017 TAX PAYMENT, INTEREST, PENALTY AND OTHER AMOUNTS: FAQ NO. 23)