What is the Islamic ruling regarding the strong presumption that the two children are not his?

The affairs of Muslim men and women should be presumed to be sound unless proven otherwise. The Sharia encourages the establishment of lineage. Since these two children were born on your marital bed, it is not permissible for you to deny their paternity after all this time. There is no weight given to mere strong suspicion. Therefore, you must discard this suspicion, fulfill their rights, and refrain from spreading any rumors about denying their paternity.