If i did a work for you...

"Work" as a noun is indefinite. You wouldn't say "a work", you might say "a job" or just "work".

"If I did work for you I wouldn't want to be paid." ("for the work" is redundant)
"If I did a job for you I wouldn't want to be paid."

You could also use work as a verb.

"If I worked for you, I wouldn't want to be paid."

Thanks a lot.
Sorry if "work" is indefinite why in the end of the sentence it is "the work"?

The first use of 'work' is noncountable, being notional or hypothetical work, thus there is no preceding article; the second use is countable, referring to the specific work done, and requires an article

If I give food to you, I want to be paid for the food.
If I supply wood to you, I want to be paid for the wood.

Thanks a lot for your help

You can put the article "the" in front of work.

If I take care of your dog, I want to be paid for the work.

More likely that people will use 'it'. If I [do something for you], I want to be paid for it.

Thank you very much

Most appreciated. Many thanks