There are several free services for getting the live price or download historical data for 1M or 1D charts.

I wonder if there is a free API service to get the data (OHLC) for a specific date of 1D chart or DateTime of 1M chart?

You can access foreign exchange rates from the Federal Reserve Economic data. You can access this open data via Enigma Public and make use of their free API. You need to sign up for an account to do so but it's free.

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