verantwortlich für = who caused something to happen. * Wer ist verantwortlich für den Unfall? > ‘Who is responsible for the accident?’
zuständig für = whose domain something is * Er ist der dafür zuständige Beamte > ‘He is the officer responsible for that (=in charge of)’.
Source: Mastering German Vocabulary
Zuverlässig means reliable, dependable or trustworthy. I don't think those are synonomous with responsible at all.
Have a look at meaning 5 at https://www.oxfordlearnersdictionaries.com/definition/english/responsible?q=responsible .
Or at the "behaving correctly" subheading at https://dictionary.cambridge.org/us/dictionary/learner-english/responsible , which gives "able to be trusted" as a gloss for that meaning of "responsible", i.e. "trustworthy".
Keep on learning English! Don't give up!
So to answer ArvindhMani: "I'm a responsible person." - "Ich bin ein veranwortliche Mensch."
No -- verantwortlich has the wrong ending: after ein, you need mixed inflection, which is -er for masculine nominative singular.
But the meaning is wrong: (für etwas) verantwortlich (sein) is "(to be) responsible (for something)" -- verantwortlich does not mean "responsible" in the sense of "I am a responsible person" (reliable, dependable, trustworthy).
There may a be tiny bit of overlap between responsible and reliable, but they are different enough to not be interchangeable in most cases. Reliable means they can be depended on to do something well or correctly. Can be depended upon / relied upon by others. Responsible, as in 'a responsible person', does not imply any kind of service to others. It could be someone who is entirely self serving, but who is sensible, takes no risks, does things correctly and looks after themselves well.
My comment above on verantwortlich was wrong, that should have been about verantwortungsvoll. I think that fits well in this case, but zuverlässig doesn't as that has another meaning.
Ein verantwortungsvoller Mensch - A responsible person.
Ein zuverlässiger Mensch - A reliable person.
In short: zuständig means something like "it's in your job description" while verantwortlich just means you were responsible for something.
For example, if you dropped a plate and broke it, you were responsible for the breaking -- but it hopefully didn't happened because you're the person who is responsible for breaking plates because that's "in your job description". So you were verantwortlich for the broken plate but hopefully not zuständig.
See also the topmost (most upvoted) comment on this page, and the other comments generally.