This is a good question. I can see where your problem is. Grammar can be tricky. The best way to answer this question is to break down the sentence. The benefit of this is you can see how the sentence is constructed.
Here is your sentence:
"I will get a reward since I passed my class."
"I" is the pronoun subject of the sentence.
"Will get" is the verb phrase of the sentence.
"A" is an article or a adjective; it depends who you ask.
"Reward" is a noun direct object.
"Since" is a subordinating conjunction.
"I" is the pronoun subject of the subordinate clause.
"Passed" is the verb of the subordinate clause.
"My" is an adjective or possessive pronoun.
"Class" is the noun direct object of the subordinate clause.
Based upon this break down, we can say that there are only two modifiers in this sentence. "A" modifies "reward," and "my" modifies "class." "I" is the subject for both the independent and dependent clauses.
I will add a link. Read the various explanations.