Candidate 1 is not normal English, and a native speaker would not use "as being" in this case, unless you meant "I defined A as 'being useful'", so that for example "I am A" means "I am being useful", but I don't think that's what you mean. If it is, please say so.
Candidate 2 claims "I defined A, and had the intention that it would be useful".
If you'd rather claim that A is useful, rather than that it was intended to be useful, as you suggest in your question, I would say "I defined A usefully", claiming that A is defined in a useful manner.
You could also say something more similar to "I defined a useful A", calling A useful with an adjective, which would probably be more natural, but I cannot give a specific example that would work without more context.
"I defined A, which is useful" would also be correct, albeit a bit clunky.
If you gave some more context, I could perhaps answer your question better.