Can I Cover My Margin Call On A Put Sale Position By Closing It With A Different Expiration Date?

No, the only way to close your position is to buy back the same exact option.

Now, you can certainly buy another option with a different expiration date, which can help alleviate all or part of your margin call, but you’ll end up with an option spread of some sort.

If that works for you, then fine. But, if you want to completely close the original position, then you need to buy back the same exact option contract.