Every time after I urinate, there is a little bit of clear discharge that keeps flowing for 15-30 minutes. My doctor said that this is due to an inflammation in my urethra. I took some medication for this, but it has not resolved the clear discharge after urination. Will my prayers be accepted if I perform ablution and pray without cleaning this clear discharge from my private parts and clothes? It is very difficult for me to always wash my private parts and clothes where they touched.

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.

The mentioned discharge is called Wadi, and the rulings applicable to urine apply to it as well; it is ritually impure and invalidates one's ablution. Everything that comes out of the front and back passages invalidates ablution, and it is all considered ritually impure (Najis), except for semen, according to the majority of scholars.

If this discharge continues to come out for the mentioned time interval only and then stops for a sufficient time to clean yourself, perform ablution, and pray, then you have to wait until it stops, except if waiting for it to stop would lead to missing the current prayer.

You may follow the opinion of Imaam Maalik in this regard; it is easier for those who find difficulty in avoiding impurities, as in your situation.

The Maaliki book At-Taaj wal-Ikleel Sharh Mukhatasar Khaleel reads:

"The impurities that are difficult to avoid or remove are excused. The command to remove them is only a recommendation, not an obligation. This applies in the case of a necessity and the continuous state of impurity like in the case of the Mustankah (i.e. the person who is suffering from incontinence because of illness, old age, cold weather or the like). Al-Mudawwanah reads, 'The impurities that are difficult to avoid or remove are excused, as is the case when urine or Mathi is often discharged unintentionally due to cold or some illness, it is obligatory to pefrom ablution, except in the case of the Mustankah, then it is recommended (not obligatory) for him to perform ablution for every prayer, like the case with the Mustahaadhah (i.e. the woman experiencing bleeding outside the monthly menses). If it is difficult for him to perform ablution due to cold weather or the like, he is not obliged to perform it (for every prayer). If the discharge is emitted during the prayer (in the case of the Mustankah), he should stop it by placing a cloth or the like and carry on with the prayer ... It is recommended for him to take precautions to prevent the discharge from staining his clothes.'"

In brief, if it is hard for you to remove the impurity in reference, then you should know that hardship begets ease and what incurs hardship is excused (i.e. the impurities that are difficult to avoid and remove are excusable) as per the Shariah. It should be noted, though, that it is more prudent to wait until the flow of this discharge stops, clean yourself, and perform ablution, as long as this would not lead to missing the current prayer.

Allah knows best.