The Oxford English Dictionary says summat is actually a way to say somewhat. The word comes in the following forms:
Forms: α. ME sumhwat, sumwhet ( Orm. summwhatt), ME–15 sumwhat (ME sumwhate, sumwat(t, 15 sumwhatt); ME sumquat, ME sumqwat, 15 Sc. sumquhat; ME somȝwat, ME–15 somȝwhatt, ME–16 somȝwhat; ME somwat, ME–15 somwatt; ME– somewhat. β. dial.17 sumet, 18 summat, summut, zum'ot, etc.
So summat is a quicker, dialect-version of somewhat made by omitting the /w/ sound. The OED uses it in in various examples, like this:
1859 ‘G. Eliot’ Adam Bede I. i. viii. 172 It's summat-like to see such a man as that i' the desk of a Sunday!
Sense: Some (material or immaterial) thing of unspecified nature, amount, etc. Now arch. or dial.
1859 ‘G. Eliot’ Adam Bede I. i. i. 10 A man must learn summat beside Gospel to make them things.
I suspect that your meaning of something for summat came from this now archaic definition. Somewhat->summat, where somewhat had an original meaning along the lines of something.