Correct spelling, explanation: the word stays appeared for the first time in late Middle English after it came from an Old French form estaye. However, the origin of the word can be found in the Latin word stare, which used to mean to stand. The base form of the word stays is stay.

Definition of stays:
1. verb (3rd form singular) – not to leave some place or a situation;
She stays at home most of the time because of three, small kids.
2. verb (3rd form singular) – to be in some place for a short time, usually as a visitor;
Every time he goes on holiday, he stays in some luxurious hotel by the sea.
3. noun (plural) – a period of time which you spend in some place;
We don’t like being in one place so this holiday we had some great stays in some hotels across the country.

Collocations with stays:
Some common collocations include comfortable stays, hospital stays, and short stays;
It was a wonderful, two-month holiday, during which we had a few comfortable stays in mountain cabins.
This year she has already had three hospital stays due to her illness.
We didn’t have much time so our trip was just a few short stays in the main cities.

Incorrect spelling, explanation: when we add an -s ending to a verb or a noun, sometimes it becomes -es. It happens when a word ends, for example, with s, z, ch, x, etc. When a word ends with a -y letter, we change it to -i and then add the -es ending only when it is preceded with a consonant. When there are two vowels at the end of the word, we only add -s. Therefore the only correct spelling is stays and not stayes.