There are valid (saheeh) hadiths of the Prophet Muhammad (p.b.u.h.) about not fasting only on Fridays, but adding Thursdays or Saturdays to it. Some of them are as follows:
Narrated Abu Hurayra: I heard the Prophet (ﷺ) saying,
“None of you should fast on Friday unless he fasts a day before or after it.” (Bukhari, Sawm, 63. Also see: Muslim, Siyam, 147; Abu Dawood, Sawm, 51; Tirmidhi, Sawm 42; İbn Majah, Siyam, 37; Ahmad ibn Hanbal 1/288, 2/422, 526.).
Narrated Muhammad bin `Abbas:
I asked Jabir “Did the Prophet (ﷺ) forbid fasting on Fridays?” He replied, “Yes.” (Other narrators added, “If he intends to fast only that day.”) (Bukhari, Sawm, 63)
Narrated Abu Aiyub from Juwairiya bint Al-Harith:
“While she was fasting on Friday, the Prophet (pbuh) approached her and asked “Did you fast yesterday?” she said “No”. The Prophet asked “Do you intend to fast tomorrow?” she said “No”. Upon this, the Prophet said “Then break your fast”.” (Bukhari, Sawm, 63; Abu Dawood, Sawm, 53)
According to these hadiths, some scholars considered fasting only on Friday as Haraam (forbidden), and some considered as Makruh (disliked). Abu Hanifa, Imam Malik, Imam Mohammad considered it as Mubah, to whom are supposed that these hadiths did not reach.
According to us, the right thing is to follow the hadiths and not to fast on Fridays only without adding Thursday or Saturday to it.