Hello @Sai Kiran Palivela
I looked at this question earlier today and thought "I know there isn't a built in parameter for this but I've written a query in Kusto Query Language that achieves the same thing, building an expression should be a walk in the park!". While I had all the logic in place from this previous query, I had to translate this into an expression with Logic Apps.
Here is my basic logic app that runs once a week (you can have it run every day if you really want). If the day it runs on matches the intended day (in this case 2 for Tuesday) and the intended week (once again, 2 for the second Tuesday of the month) then it returns true, otherwise it will be false. This does mean that the logic app needs to run the trigger at least once a week on the Tuesday, but the condition statement will evaluate and terminate the workflow if it isn't the second Tuesday of the month.
I've provided a copy of the logic app for you to test / copy https://github.com/TheAlistairRoss/AzureMonitor/blob/main/LogicApps/DayOfTheMonthTrigger/template.json
If you want the expression found in the Condition statement, it is
if(equals(startOfDay(addDays(if(less(addDays(addDays(startOfMonth(utcNow()), int(concat('-',dayOfWeek(startOfMonth(utcNow()))))),int(variables('Constants').DayOfWeek)), startOfMonth(utcNow())),addDays(addDays(addDays(startOfMonth(utcNow()), int(concat('-',dayOfWeek(startOfMonth(utcNow()))))),int(variables('Constants').DayOfWeek)),7), addDays(addDays(startOfMonth(utcNow()), int(concat('-',dayOfWeek(startOfMonth(utcNow()))))), int(variables('Constants').DayOfWeek))),mul(add(int(variables('Constants').WeekOfMonth),-1),7))),startOfDay(utcNow())),true,false)
kind regards
Alistair