Hello Mr. Hadi
'The event took place at 11.30am local time.' The kind of time ('local time', 'Beijing time') is put right after the time itself.
'In', 'at' and 'on' are easily confused. Bare in mind, we are talking about prepositions of time here. These can be used as prepositions of place as well. So, never mind, for time:
'In' is for years, centuries, seasons, months and parts of the day ('in the afternoon'). 'At' is for times, meals, festivals ('Easter') and periods of time. 'On' is for all the days of the week, special days ('New Year's Day') and dates.
I hope that helps. Have fun.