Insist and Persist

➤ Rule 1 :
Insist on / that - to hold up someone's claim emphatically

~ He insists on his innocence.

~ He insists that he is innocent.

 Insist on/that - to demand continually 
~ She insisted on carrying her own bag. 

➤ Rule 2:
Persist in - to continue to do something in spite of difficulties or bad feedbacks

~ He persists on crossing the river in a very windy weather.

Persist with - to work ceaselessly

~ Ruma persists with her study to get BCS cadreship.

➧Again in the view of parts of speech:

Persist - a situation with remaining last ( same) condition. 

 ~ The cold wave is likely to persist for another week.

Persistence (N) - standing with firm determination

Insistence ( N ) - the state of being insistent

Persistent (Adj) - determined to continue to do

Insistent (Adj) - urgent

Insist (v) - demand something forcefully

Persist (v) - continue in an opinion or course of action in spite of difficulty or opposition.