Incorrect spelling, explanation: word asign looks like it’s built similarly to words such as ablaze, where the prefix a- means on or in, or in some contexts no (like in atheist = non-theist). The double s stemming from the Latin origin of assign is characteristic and makes the word recognizable as a separate item, which is why assign is the correct version.

Correct spelling, explanation: the word’s origins trace back to the Latin word assigno, which, as many other Latin words, is characteristic because of the structure and the double s. The word lost its Latin suffixes, but the double s stayed because in general, it’s easier to shift the vowels and suffixes, but leave the base word relatively similar to the original, hence assign is so similar to its predecessor.

Definition of assign:
verb
1. to designate a task or a thing to a person
I’m going to be late, my boss decided to assign a whole lot of paperwork to me.
2. to set something aside for a specific purpose
When I bake I always assign a special double-chocolate batch only to children.