I would like to know which of the following sentences is correct.
If you had come tomorrow, I might have been able to help you.
If you came tomorrow, I might be able to help you.
The following three sentences mean different things.
If you had come tomorrow, I might have been able to help you.
This sentence is a counterfactual. It means that, because you came today instead of tomorrow, I can't help you. And there is no chance that I can help you if you come back tomorrow—you lost your chance for help by coming on the wrong day. Or maybe you have a deadline; tomorrow is too late.
If you came tomorrow, I might be able to help you.
If you come tomorrow, I might be able to help you.
These both mean that I can't help you today, but if you come tomorrow, there is a chance that I will help you.
The difference between them is in my perception of how likely it is that you will come back tomorrow. If I think it's very unlikely, I would use came. If I think it's very likely, I would use come. And for moderate likelihoods, either tense works fine.
Someone else posted an answer here that seemed sensible, then deleted it for some reason. The rules were as described in this website:
http://www.myenglishpages.com/site_php_files/grammar-lesson-conditionals.php
(1) real conditional:
"If" + simple present, (then) + simple future.
If you come tomorrow, I will help you.
(2) unreal conditional:
"If" + simple past, (then) + would* + base verb.
If you came tomorrow, I would help you.
note: could, should and might can all be substituted for would here, but the meaning changes slightly.
The next rule is instructive, although it doesn't relate to the question, because it must occur in the past.
(3) impossible conditional referring to past
"if" + Past Perfect, + would + have + Past Participle
If you had come yesterday, I would have helped.
Number 2 is more correct than number 1. In number 2, as the subjunctive form of come, came is considered to be "correct" usage here, but the indicative come is more often heard. "If you come tomorrow, I might be able to help you.
Regarding number 1, the introductory clause is usually said/written as "Had you come tomorrow,". In addition, the construction is generally used more in the past tense than in the future tense, because it implies a counterfactual situation. Future events are not (yet) counterfactual, so "Had you come yesterday, I might have been able to help you." is correct.
Oddly, when "if" is used for past subjunctive, the past tense came is used, e.g. "If you came yesterday, I didn't help you." For future subjunctive with "if," either come or came can be used, but I think come is more often used. i.e. "If you come tomorrow, I will help you." is heard more than "If you came tomorrow, I would help you."
https://en.m.wikipedia.org/wiki/English_subjunctive cf. "Distinguishing from past indicative after if"
Using auxiliary/helper verbs in the adverbial phrase "might be able to help" complicate things just a bit more. "Might be able to help" is the indicative, and can substitute for "will" in the example above. "Might have been able to help" is the past subjunctive case that can substitute for "would".
The first sentence is incorrect,because a counterfactual conditional is a proposition which states what would have followed had the actual sequence of events or circumstances been different. Referring to future you can use either a real conditional
If you come tomorrow,I will be able to help you.
or an unreal conditional
If you came tomorrow,I would (could,might) be able to help you
As events in the future have not happened yet, we cannot refer in the IF-clause to a counterfactual future action or state. However infinitesimal the possibility, it exists, and therefore can be presented only as a hypothetical, not as a counterfactual action or state. #53ais therefore a possible utterance, #53b is not:
53a. If the sun exploded tomorrow, the solar system would be destroyed.
Incorrect.
53b *If the sun had exploded tomorrow, the solar system would be destroyed.
With past counterfactual situations, IF is sometimes omitted in more formal English, and subject and verb are inverted:
Had I saved more [in the past],I would retire next year.
Had Watson not bungled that interview last year, he would be the anchorman now.
Had it had been fine yesterday, we would have had a barbecue
https://www.usingenglish.com/articles/conditional-sentences-in-english-5.html