Final answer:
Poland was the country that directly supported the False Dmitry(s), specifically during the early 17th century to extend its influence over Russia.
Step-by-step explanation:
The country that directly supported the False Dmitry(s) was Poland. During the Time of Troubles in the early 17th century, the Polish-Lithuanian Commonwealth saw an opportunity to extend its influence over Russia by supporting the False Dmitry(s), who claimed to be the legitimate heirs to the Russian throne. Although there were three individuals who assumed the moniker of False Dmitry, it was primarily the first False Dmitry who received significant backing from the Polish nobility and even married a Polish noblewoman, which lent him additional legitimacy in the eyes of many Poles.
During the Time of Troubles in the early 17th century, Poland indeed played a direct role in supporting the False Dmitry(s) as part of its strategic interests in extending influence over Russia. The Polish-Lithuanian Commonwealth perceived an opportunity to assert control by backing claimants to the Russian throne who presented themselves as legitimate heirs. Among the various individuals who assumed the identity of False Dmitry, the first one received substantial support from the Polish nobility. Notably, he went as far as marrying a Polish noblewoman, further legitimizing his claim in the eyes of many Poles. This support from Poland contributed significantly to the political complexities and conflicts during the Time of Troubles, a period marked by political and social upheavals in Russia.