Can pepper cause penile discharge?

Not sure: Where are you putting the pepper? Oral ingestion shouldn't have an effect on discharge.

Applied how?: If you inserted pepper in the urethra, yes, as it attempted to remove the irritant that does not belong there. If you mean eating pepper (of any kind), then no, you have another reason for your discharge and should see your dr / urgent care / std clinic or urologist for exam and testing.