The correct word is wish.  You are referring to two different subjects, Jasper Research, Ltd. AND its affiliates.  Because of the AND, you have plural subjects.  So, the verb needs to be plural.  And with verbs, it is a bit backwards: if the verb is plural, it doesn't have an "s" on the end, whereas if it is singular, it does.  For example, "The cat drinks from the cup"--cat is singular, and the verb drinks has an "s" on the end.  However, if you have the sentence "The cats drink from the cup"--it is the opposite.  It is a plural noun (cats), and the verb drink does not have an "s" on the end.  That's how I remember it.  If you have plural subjects doing the action, or the verb, it is backwards from what you would think, and there is no "s" on the verb.  So, in your sentence, because there are two subjects joined by the conjunction "and", you need the plural verb, which in this case, is "wish".

I hope that those thoughts help a bit; the English language is very tricky and confusing, that's for sure!  Good luck.