The highlighted word is a/an persevering is highlighted a) participle b) coordinating conjunction c) gerund d) modal

The word is represented out of a context, so it's better to consider all its roles in a sentence. It can be both present participle which has the 'ing' form of the verb and gerund which is a verb that functions as a noun. It depends on how it is used in a sentence.

The answer is likely C) Gerund. A gerund is a noun that ends in -ing, essentially turning a verb into a noun. Conversely, the present participle is a progressive verb ending in ing that functions as a noun. In order to know for sure, consider the context. 

Example of a gerund:
His walking has really improved. Ice-skating is his favorite sport.

Example of a present participle:
What are you doing? I am walking to school.