This is the 16028th most frequent Russian word.
путинского
"Of Putin" or "Putin's."
The word 'путинского' is used as a possessive adjective describing a plan related to Putin.
Мы обсудили путинского плана мирных переговоров.
We discussed Putin's peace negotiation plan.
Here, 'путинского' modifies the noun 'сторонника', indicating a person who is a supporter of Putin.
В произведении описан портрет путинского сторонника.
The work describes the portrait of a Putin supporter.
In this case, 'путинского' is used to attribute the noun 'режима' to something associated with Putin.