When does a wife's postpartum bleeding (nifas) end if brown discharge is present, and is intercourse in this state a sin?

One must ascertain the rulings of Islamic law before undertaking any matter. Yellowish and brownish discharges connected to post-natal bleeding (nifas) are considered nifas as long as they occur within the forty-day period. You erred by engaging in intercourse with your wife while she was in her nifas period. You must offer sincere repentance for your shortcoming, and no expiation (kaffarah) is required of you due to your ignorance of the ruling.

Nifas ends with the cessation of blood and any associated yellowish or brownish discharge, or upon the completion of forty days. If a woman experiences purity before the forty days, intercourse with her is permissible. If bleeding extends beyond forty days without purity, she is considered to be experiencing irregular bleeding (istihada), unless it coincides with her regular menstrual cycle.