Mary’s so-called request for fasting on Wednesdays and Fridays has only been made in unapproved private revelations, to my knowledge. There is another unapproved private revelation where she also requested fasting on Mondays. The rules of the forum forbid posting material from unapproved private revelations, so I will not discuss it further here. Your priest should not be presenting these unapproved revelations as if they’re approved, but it’s possible that you quoted him out of context or misunderstood something he said, so I will give him the benefit of the doubt since I wasn’t there to hear it myself.
Mary, in various Approved private revelations, has called on us generally to do penance in reparation for mankind’s sins, for the Holy Souls in Purgatory, and for the Holy Father. To my knowledge, she has not requested fasting specifically in these Approved private revelations, but has simply requested “penance”, which could be fasting or could be some other penance of the person’s own choice. She has also expressed in one or more Approved private revelations that people should follow the teachings of Christ and the rules of the Church, including the Church rules for fasting and abstinence on the days and in the manner required by the Church.
Mary has called on people in various Approved private revelations to pray the Rosary and to make the First Saturday Devotion, which does not involve fasting (except for the usual Church-required one hour fast before receiving Holy Communion). Many people make this devotion and some of them make it over and over by starting a new Five First Saturdays each time they finish the previous set of 5. This is a good way to honor Our Lady and to build good prayer and confession habits, if you choose to do the devotion.
http://www.themostholyrosary.com/appendix2.htm
Keep in mind that Catholics are not required to believe or follow any private revelations, even if they’re approved.
And in the case of unapproved private revelations, many Catholics prefer to wait until the apparition or revelation is Church-approved in some way before they get involved with it. Some apparitions are “Approved for Faith Expression” which means the apparition itself has not been approved or disapproved, but the faithful are permitted to do a particular devotion associated with it.
If you choose to fast as your own personal private devotion or penance, I recommend as always checking with your doctor to make sure that what you want to do will not be harmful to your health.