I had previously raise a similar question like yours and i've got it implemented successfully through the advice here http://www.tersus.com/?Id=7905
In my opinion, for your case maybe you can for every 86400000 ms (24 hrs) or 6 hrs or 12 hrs, check if its a Friday.
If its a Friday, check every 900000 ms (15 mins) or finer intervals to see if 10AM or current time hours at 10. If it is, start the process and write the timestamp that its started running to database (and maybe time it ended running if you want to track duration of process)
Also on the check on if its a Friday, you can look at the timestamp to check if it has been run for that Friday, if yes, then skip the check every 15 mins.
I suspect the granularity of the intervals might have an impact or accuracy, so i suggested various intervals. You can do some testing for verifcation.
You can trigger the start for every 24 hrs check at the startup of the application as seen below in green highlight.
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