Will the child born of adultery enter Paradise, and what is the authenticity of the Hadith: "Neither a disobedient child, nor an alcoholic, nor a reminder of favors, nor a child born of adultery will enter Paradise"?

A child of adultery, like any other person, if he does good, he will receive good, and if he does evil, he will be accountable for his evil. He is not responsible for what his parents did, as Allah Almighty says: "And no bearer of burdens will bear the burden of another." As for the hadith (definition), "A child of adultery will not enter Paradise," it is weak or fabricated. Even assuming its authenticity, it is interpreted to mean someone whose sperm's impurity caused his corruption and failure to do good deeds, or it was said about a specific person who harmed the Prophet, peace and blessings be upon him, or it is a form of threat to the adulterer.