Correct spelling, explanation: considering the origin of this word, we certainly say that solely the form warranty is correct. In English, the first known use was in the 14th century but it has roots in the Germanic language spoken by Franks. This word also existed in Old North French as warantie indicating protection or safeguard. As you can see, there is the vowel a in this word, not e. Therefore, warranty is written correctly and warrenty is misspelled.

Definition of warranty:
noun, a document giving a guarantee that a defective product will be repaired or replaced
The fridge is still under warranty.
Can you give me a warranty for this car?

Definition of warranty:
breach of warranty – violation of an implied contract to fulfill guaranty; the terms of a promise or claim concerning the quality of the product;
My parents brought an action for breach of warranty against the company which had sold them the computer.
an extended warranty – a contract with consumers providing the additional service of replacing or repairing goods that fail within the extended period;
They sell smartphones to customers with one year warranty but you can also buy the extended warranty, which costs $28 every month.

Incorrect spelling, explanation: the word warranty is very similar to the word guarantee. Taking into account the history of the language, these words were the one and the same. The root of both words is in Old French and that is the reason why we spell the word warranty with the vowel a not e. Thus, warrenty is incorrect form.

Incorrect spelling