All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The fluid you have referred to is impure since it is discharged from one of the front and back passages. In principle, anything that is discharged from either passage is impure. A group of scholars held that the basic principle in this regard is that whatever comes out of the front and back passages is deemed impure, with a few exceptions which are considered pure by supportive evidence.
Ibn Qudaamah said: “Discharges from the front and back passages such as urine, stool, Mathy (pre-ejaculatory fluid), Wady (white prostatic fluid), blood, and other discharges, are all impure by consensus of the scholars with a few exceptions that we shall mention later, Allaah willing.” [Al-Mughni]
Shaykh Ibn ‘Uthaymeen said in the context of highlighting the supportive evidence of the scholarly view that the moisture of the private parts is impure: “They supported their view by the fact that all the discharges that come out of the front and back passages are in principle impure except those considered pure by religious evidence.”
Since the fluid which you have referred to is impure, the basic principle requires that you purify your body and clothes from it before performing prayer, because ritual purity is one of the requirements for the prayer's validity and the non-fulfillment of any of those requirements renders the prayer invalid. When someone knowingly performs prayer in an impure garment and is able to remove it, his prayer is invalid due to the non-fulfillment of the requirement of ritual purity. Hence, he is obliged to make up for that prayer unless the impurity was insignificant or it was difficult to avoid it as is the case when one suffers from incontinence, i.e. impurity which comes out of the body unintentionally such as urine, Mathy, semen, and excrement that flows from the private parts on its own. Some jurists held that such impurities are excusable and, for those who suffer from obsessive whisperings, there is no harm in having recourse to this scholarly view.
The Maaliki scholar Muhammad ‘Ulaysh said: “Any impurity that one finds difficulty in taking precautions to avoid is excusable. This is a general Fiqh-related principle that is further explained by the following examples. For instance, when normal discharges such as urine, Mathy, Wady, semen and small amounts of excrement come out of the usual passages inadvertently and constantly on a daily basis once or more and touch the body or clothes, they are excused and disregarded.” [Minah Al-Jaleel]
The Hanafi scholar Al-Baabarti said:
“Impurity the size of a dirham or less of intrinsically impure substances such as blood, urine, alcohol, excrement of poultry, donkey's urine, and the like is excused and disregarded and it is permissible to perform prayer when such an insignificant amount of impurity touches the body or clothes; however, if the impurity exceeds this amount, it must be removed before performing prayer.” [Al-‘Inaayah Sharh Al-Hidaayah]
If the fluid you are experiencing stops flowing before the end of the prayer time, then you are obliged to wait until it stops flowing, perform ablution and pray. But if it flows constantly so that you cannot find any interval time to perform the prayer in a state of complete purity before the end of the prayer time, then you should perform ablution after the time of the prayer starts and pray, and whatever is discharged during the prayer does not affect you.
Please refer to Fatwa 82518 about the difference between semen, Mathy, and Wady. Please refer also to Fataawa 246277 and 87360 about the purification of the person suffering from incontinence.
Allaah Knows best.