Correct spelling, explanation: consent is the correct form, because of Latin consentire. There is no need to put c between s and e, although there is a word scent, that is pronounced just like -sent in consent. Conscent is incorrect as the origin points to consent as the correct form.

Definition of consent:
noun, permission
We don’t have the town’s consent to build a supermarket here.
Please bring the written consent from the Board.

Incorrect spelling, explanation: this form is incorrect because there is no pronunciation nor historical reason to put c in the middle of consent (from Latin consentire). While the word scent is pronounced similarly as -sent in consent, conscent is an incorrect form.