Getting away from religious concepts, of course omniscience is a logical paradox.
For example you can logically not know whether the statement "This statement is not provable" is true or false. "Knowing" that it is true implies that you have some basis upon which you know that or in other words that you have proven it to yourself in some way. But if that is the case you would have prove for something not provable, which is a contradiction.
If you knew it is false, that would mean you have disproved it somehow. But if it were false that would imply that the statement was provable and as such true. So you would have shown that a true statement was false and hence reached a contradiction.
That is more or less the strongly simplified way my linear algebra professor explained
Gödel's incompleteness theorem to us in the second reading.
Other typical examples of things one can logically not know is, if the
ZFC Axioms are true, that the ZFC Axioms are true or
the continuum hypothesis using only the ZFC.
So since there are things that can logically not be known (which has to be established first for this reasoning!) an omniscient being is of course a paradox.
Though one shoud say that is only the case if omniscient is defined as "knowing the truth value of every statement", like it usually is in the absolute cases we discuss here. There are also people who like to define omniscient only as "knowing the truth value of every statement of which one can know the truth value", which is, due to obvious reasons, not paradox anymore.
Even though a paradox for our cases it is of course possible for it to be "questionably true", just like we have "questionable omnipotence".