What is the ruling regarding the fluid that is discharged during Tawaf in the daytime in Ramadan as a result of men and women pressing against each other in the crowd?

If you felt something egress during circumambulation (Tawaf) and it was merely a doubt, this does not affect the validity of your ritual purity (Tahara) nor your Tawaf, because certainty is not removed by doubt. Touching a non-mahram from over a barrier does not invalidate ablution (Wudu).

However, if you were certain that something exited, then your Wudu is invalidated, and you must exit, purify yourself, renew your Wudu, and resume your Tawaf, because ritual purity is a condition for the validity of Tawaf according to the majority of scholars. In this case, if you completed the Tawaf and Sa'i without ritual purity, your 'Umrah is incomplete, and you must return to Makkah to complete it, or you would be considered in the ruling of one who is prevented (muhsar) if unable.

It is permissible to adopt the view of those who consider purity for Tawaf to be sunnah, like Ibn Taymiyyah, which means the Tawaf is valid despite the invalidation of purity. This less preferred opinion may be adopted when rectification is impossible.