Is the following sentence grammatically correct?
If I were president of this country, I would have made everyone in this country rich.
What I mean is "if (something happened in the past) then (effect of that event in the present)."
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No, OP's example isn't "correct", because the verb forms are inconsistent. The consistent versions are...
1: "If I were president of this country, I would make everyone in this country rich"
2: "If I had been president of this country, I would have made everyone in this country rich"
In #1 the speaker is postulating an "unreal" situation in which he is president at the time of speaking, but in #2 it's when he was president (also unreal, since he never was, but crucially, it's in the past).
Note that technically speaking, #1 is a "true" subjunctive usage. The equivalent past tense version for #2 would be "If I would have been president", but almost nobody ever says that, because we increasingly tend to avoid the subjunctive. People still commonly say things like "If I'd have been president", but in my experience if you ask what that 'd stands for they'll often say it's a shortening of if I had have been (which is grammatically nonsense, but it just goes to show we don't like the subjunctive).
To express what you want to say, you should say:
If I had been president of this country, I would have made everyone in this country rich.
This sentence is similar to the following one (See How to ask the question in conditional sentences?)
Would Chinese people have loved tradition if China had not been a communist country?
"If I were president in this country" introduces an irrealis, something that will never happen; in that case, you should write "I would make everyone in this country rich."
It is similar to the following sentence.
If I were rich, I would live on Long Island. I am not rich, and I will never be rich; therefore, I will never live on Long Island.
This is different from the following sentence.
If I take the 6:00 PM train, I will arrive in time. There is a chance I can take the 6:00 PM train; therefore, there is a chance I will arrive in time.