The Prophet ﷺ was brought some fadikh (a date drink) in the mosque, and he drank it. That is why it came to be called the Mosque of Fadikh.
حدثنا وكيع حدثني عبد الله بن نافع عن أبيه
أن النبي ﷺ يعني أتي بفضيخ في مسجد الفضيخ فشربه فلذلك سمي
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Its chain of transmission is daif, due to the weakness of Abdullah bin Nafi. The hadith is found in Majma al-Zawaid 4:120, where it is stated, "Ahmad and Abu Yaala related it," then the wording of Abu Yaala is given, and Abdullah bin Nafi is in it. The majority declared him daif, though some said his hadith may be recorded.Al-Fadeekh, with fatha on the fa and kasra on the dotted dad, and ending in a dotted kha as well, is a drink made from crushed unripe dates, that is, dates that have been mashed, as stated by Ibn Athir. As for Masjid Fadeekh, it was already mentioned, in what we quoted from Hafiz in his commentary on 5601, that it lies east of Masjid Quba. In Khulasat al-Wafa by Samhoudi, 267-268, it is stated that it is a small masjid east of Masjid Quba, on the edge of the valley, on a raised piece of ground, built up with black stones, and it is square in shape, measuring eleven cubits between east and west, and from the qibla toward Sham and thereabouts.