How would they know the screen is replaced?
I can't afford that!
Your warranty won't be voided unless they know it was replaced.
The only way they will know is if you have it serviced and they take it apart at the Apple store, if you take it in for some other issue a Genius won't know it is not a OEM screen, but if there are signs of it being replaced then they will know. Basically if there are any marks on your phone showing obvious repair it will pop up a red flag.
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Although my iPhone is still under warranty I don't think apple cover this,
so a)
how much do they charge?
b) is there a a cheaper option as I'm not in a good financial position right now
Is it a 5 or 5s ?
The only issue with screen replacement is that most of the "cheap" replacement shops only offer a 30 Day warranty on the screen itself. I have seen replacement as low as $99, but as high as $169 with a lifetime warranty.
The other downside is that this is a cheap aftermarket replacement screen, so it won't be as crisp and clean as a apple supplier one.