Which sentence is correct if my intention is to express the continuing process : English is studied by me for several years or English has been studying by me for several years.
English has been studying by me for several years.
This is not valid English: has been studying is active voice and will not sustain the agentive complement by me.
English is studied by me for several years.
This is formally acceptable, but there is a semantic disconnect between present-tense is studied and the temporal for several years. It is quite possible for a 'gnomic' present to refer to an indefinitely long timespan, but that timespan is taken to extend equally far into the past and the future, while for several years implies that the span has come to an end. The only context in which this sentence might appear is a narrative cast in the 'historical present': perhaps a chapter heading in your autobiography!
English has been studied by me for several years (suggested by Weather Vane)
This is possible: it might be a continuative perfect, mentioning an activity which has continued right up to the present. Equally, however, it might be an existential perfect, mentioning an activity lying entirely in the past: that activity would bear perfective aspect and thus exclude your requirement that it express processuality. There is consequently a growing tendency in present-day English to cast continuatives in the progressive perfect:
English has been being studied by me for several years.
All of this begs the question of whether I have been studying English can be meaningfully cast into the passive at all. What passivizable thematic role does English play here? A field of study is not a Patient or a Theme, unless the Agent effects (or at least seeks to effect) some change of state in it, as in This problem has been studied by me several years—and that doesn't really work in the progressive. English is I think more like a Location or Scene, and it's very doubtful that that can be passivized: *The airport has been departed from! I cannot imagine circumstances in which such a sentence would actually be uttered.