"As of this morning" vs. "as at this morning"

AS of: Used to indicate the time or date from which something starts:

• As of January 1, a free market will be created.

• I’m on unemployment as of today

Source:oxforddictionaries online

Your second sentence is wrong.

I suppose both are correct. I have heard both used by native English speakers. I prefer the first to the second but that is probably because I am English and the second sentence sounds American, or at any rate not British.

"As at" is mostly used in stats and finance. It indicates a bi-temporal slice of data and thus has two time references buried in it. It really translates to "as of a certain time, I knew something about some other time."

For example, let's say that on Jan 1 I had $20 in my bank account, and project it to be $25 on Feb 1. Let's now say that on Jan 2 you found out it would still be $20 on Feb 1.

You would say that as at Jan 1 my bank account is projected to be $25. As at Jan 2, my account is projected to be $20.

As of Jan 1, however, I only have $20.

I agree, it sounds odd, but it does have a limited purpose.

"as of" can be ambiguous. "as of" and "as from" can easily be understood in their meanings of "valid from this time onward". "as at", by contrast, means "this information was valid at that particular time, but I can't vouch for it after (or perhaps even before) that point". Many people use "as of" more casually for the same thing, but if you want this specific meaning to be absolutely clear, particularly in an academic or statistical context where changes may occur over time, using "as at" is unambiguous, and to my mind preferable.