Hi Goodman.
I have been living in California since 3 years ago = that'll be so unacceptable in my camp.
I have been living in California for the past 3 years. = that's acceptable and will make a student pass their English test in a non-native land.
Yes, the word 'ago' with a present perfect tense, will appear to be a direct translation from a dialect or another language usually non-native
English. I see this being practised.
cheers.