Correct spelling, explanation: the word has its origins in a verb attend (to be present, to participate) and a suffix -ance, which has two major tasks: to create a noun and represent quality of. Thus any other form than attendance is wrong.

Definition of attendance:
1. noun: the fact that some people are present, for example on some event, meeting, party or school
She undermined my attendance in church last Sunday! What an insult!
2. noun: number of people who participate in something (for example a meeting or an event)
Philosophy may be boring, but attendance on my lecture is higher than I expected.

Idioms and phrases with attendance:
→ to dance attendance on, to do everything in your power to please somebody or to make their life as easy as possible: Sometimes I can’t stand my husband- although he is an adult man, he still needs someone to dance attendance on him.
→ to be in attendance, to take part in some important, often very official event: Some important ministers was in attendance on this conference.
→ to take attendance, to check, for example at the beginning of the classes at school, if all students from the list are present: Our professor always takes attendance at the very beginning, so then he knows who was late.

Incorrect spelling, explanation: the word is a noun created form the verb attend, which can be explain as take part in, be somewhere, for example, on a party, meeting, event, etc. by adding the suffix -ance, that is very helpful while creating nouns from verbs. Taking it under consideration, it is definitely mistaken to turn a into e, as there is no such word as attendence; attendance is the only correct spelling.