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I did a research study on one important filed. I would like to said that my study is the first study that did two things.

For example: "This is the first study that: 1) applied X method to the Y filed, 2) study the impact of A on B using the X method."

Is my sentence, correct? if not, how to improve it?

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I think you meant to write "field" instead of "filed".

You have a change of verb form from 1) "applied" to 2) "study".

It might be as well to use two clauses coordinated by "and", and with a different verb form. If it's introducing new material, it might even be good to expand the sentence, rather than contract it, so...
"This is the first study to apply method X... and the first to examine the impact...".

Using "examine" or "look at" will avoid re-using the form "study" as both noun and verb, in what amounts to "the first study to study...".

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