Reichsarbeitsdienst Bezirksarbeitsführung (Local area work Administration) RADBA-F. The last F is either from führung (an alternative abbreviation then BA, F for Frauen or F for a place like Frankfurt am Main.
1 Essen = 1 meal, but I doubt the clothing or procurement office would give out meal tokens or even have such a depart abbreviation within the RAD as an Amt, an Amt would be equal or higher than the RAD, having the BA part after RAD implies subordination, so I think your theory on that part is wrong.
An abbreviation of BA-F as Bezirksarbeitsführung is possible, but unlikely as it implies that there is then a distinction between a token (or abbreviation) with just BA with the same meaning and then no other context. So I think this isn‘t likely.
F for Frankfurt is possible as here is an example of RADBABr (but with no hyphen) which dictates Brandenburg. This is likely, but handing out meal tokens to everyone working in that area is over the top administration.
https://www.weitze.net/militaria/82/Reichsarbeitsdienst_RAD_Sporthose__508082.html
F for Frauen might be a possibility as women might have been given extra rations or care while in this service, the meal token might have been a way of confirming they had been fed or to get something extra in the meal in an organised controlled manner. This is also likely, but not more than F for Frankfurt.
To find the actual meaning would need more research, likewise someone could have just made it themselves, either during the time of the RAD or anytime afterwards to sell as NAZI Memorabilia.
https://en.wikipedia.org/wiki/Reich_Labour_Service
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