Should and were to can also be used in the if-clauseA group of related words containing a subject and a verb. of third conditional sentences. To express that the sentence refers to past, however, a perfectThe aspect expressing completion. E.g.: He’s finished university. infinitive is used after them. Note that this usage (like the situation it expresses) is not very common.

SHOULD

Should can be used after in case to emphasisSpecial importance or attention given to something. E.g.: All I wanna do is have some fun.e unlikelihood. This use is rather formalNot belonging to colloquial or everyday speech; official. E.g.: I demand that Mr Smith call the person on whom the committee has decided. or may even sound archaic to some speakers.

SHOULD

Should + perfectThe aspect expressing completion. E.g.: He’s finished university. infinitive can be used to emphasisSpecial importance or attention given to something. E.g.: All I wanna do is have some fun.e unlikelihood in the past. This use is rather formalNot belonging to colloquial or everyday speech; official. E.g.: I demand that Mr Smith call the person on whom the committee has decided. or may even sound archaic to some speakers.

In first conditional, happen to and should is used to express unlikelihood.

If you happen to see Kate, could you ask her about my CD?
If you should see Kate, could you ask her about my CD?
If you should happen to see Kate, could you ask her about my CD?

The last one is the least likely.

Instead of would here it is possible to use could (ability or possibility), should (obligation) or might (possibility).

George could have won the race if his shoelace hadn’t come undone.

Instead of would here we can use could (permission or ability), might (certainty/uncertainty) or should (obligation).

If you were taller, you could play for the Lakers.
If you weren’t under 18, I should punish you.

In the if-clauseA group of related words containing a subject and a verb. of the first conditional we can use should (to express that the condition is less likely), can (permission or ability), will or would (willingness, insistence and refusal), must (obligation) or may (permission).

Instead of will here we can use may/might (certainty/uncertainty), may (permission), can (permission or ability) or must/should (obligation).

Should + perfectThe aspect expressing completion. E.g.: He’s finished university. infinitive is used as a polite expressionA word or group of words used in a particular situation. E.g.: Good morning, at six, on the sofa of thanks on receiving a gift or a favour.

"I've brought some wine."
"Oh, you really shouldn't have!" 

VerbA part of speech that expresses an action or a state. E.g.: John seldom plays tennis.s of thinking with should are used to make an opinion less direct.

I should think that the black one would go well with the colour of your hair.