"support to" vs. "support of"

The most common preposition between support and the "beneficiary" is in fact for, but in OP's construction many people might like to avoid repeating this after "Thank you for...".

There's no special grammatical rule saying which other preposition is "correct". I'd probably just use for anyway, but either of and to would be "acceptable". Or you could sidestep the issue by using something like in respect of, regarding, or with regard to.

I prefer "of." It's the more common locution in this type of statement, and it reflects the philosophical, ideological tone of the sentence. "To" feels more transitive and related to the actual incidents of (presumably) sending money, which isn't precisely what the writer is thanking the benefactor for.

Either is acceptable, depending on the precise message you wish to convey.

If I am in support of the John Q. Public scholarship, then you could thank me for my support of it.

Thank you for your continued support of the John Q. Public scholarship.

However, if I instead give my support to the scholarship, you would thank me for the support to it.

Thank you for your continued support to the John Q. Public scholarship.

To further clarify, and to make the statement sound "better", this particular statement might be more appropriately written as:

Thank you for continuing to give your support to the John Q. Public scholarship.

As FumbleFingers put it, "for" would be an acceptable, possibly "better" use, in place of "to" specifically, as follows:

Thank you for your continued support for the John Q. Public scholarship.

In this particular case, as they are all technically correct, another major factor involved is which statement you believe sounds more correct. The average person is not going to look in-depth into the nuances of what, exactly, you are saying, so in this particular case, you are probably better off using whatever sounds best to you, and by extension, what sounds best to those in your local area or in your field. This is a colloquial issue - personally, I prefer "of", and I believe that particular statement fits in best in the Northeastern region of the United States.