Is it permissible to fast alone on a Friday to make up for days missed in Ramadan due to breastfeeding, given that this day is the only day off and it is not possible to fast two consecutive days?

Muslim narrated from Abu Hurayrah (may Allah be pleased with him): "Do not single out the night of Friday for standing in prayer among all other nights, and do not single out the day of Friday for fasting among all other days, unless it coincides with a fast that one of you normally observes."

This hadith is evidence for the dislike of singling out Friday for fasting, unless it coincides with a fast that the individual regularly observes. Fasting on Friday alone is valid but disliked. It is better to fast on the day before or the day after to remove the dislike. If you are unable to do so, then fast it as a make-up (qada') fast, and there is no harm in that.