Yes you can. You can write anytime upto 3.30pm on the expiry day.
@Aastro, BSE unlike NSE(monthly contracts) has weekly option contracts. Options that expire thursday every week.
Yes you can write/sell options any day. You can write/sell on expiry day too before close of trading.
But I dont understand the part u said about "weekly on BSE’, in your question.
Thanks Nithin for clarifying that.