The correct one-word substitute for an extra profit or allowance additional to a main income etc. is perquisite.

• Perplexity means a state of confusion or bewilderment.
• Persecute means to harass or punish someone, especially because of their beliefs.
• Persevere means to continue in a course of action despite difficulties.
• Perquisite means a benefit or advantage that is additional to one's salary or wages.

Perquisite is the most appropriate word for this group of words because it specifically refers to an extra benefit or allowance that is given to someone in addition to their main income. The other words do not have the same connotation of additional compensation.