I have heard previously that, it had some theological affects on Judaism, but I know nothing about it.
I suspect what you've heard may actually be the reverse:
The renewed interest in scripture and focus on the literal and written word sparked by reformation - required early reformers to come up with new interpenetration that could reconcile the two (very different) texts of the Old and the New testaments into a new single coherent theology that would be in line with their new ideas.
Early reformers such as Calvin and Luther thus engaged in theological debates with prominent Jewish Rabbis over the meaning of verses in the Old Testament - their writings suggest they believed that not only would this allow them to gleam insight into the ancient Hebrew texts from the Rabbis - but that ultimately the Rabbis would see that in fact the Old Testament contains undeniable proof that JC was the son of god and true and final prophet (the Messiah). They had hoped this would lead the Jews who have previously resisted conversion due to the corruption of the Catholic Church to be won over by the pure arguments and pure souls of the reformers and convert en-masse. (The Rabbis hoped the reverse would happen.)
The disappointment and disillusionment of the early reformers at the failure of this to materialize (evidenced by their quite venomous later antisemitic rhetoric) gives some evidence that while the Jewish bible and Jews featured fairly prominently in early Protestant theology and writings - the opposite was not true.
I would also add - that while individual Jews have converted to both Christianity and Islam throughout history - Jewish theology has proved quite unwelcoming to new ideas coming in from other religions and from Christianity in particular. The practice of Jewish theology and debate through the middle ages (and to a degree even up to present days) takes place inside Synagogues and Midrsahas (by men only) inside very protective and closed-nit communities - not lending itself very well to outside influence .
It could be argued that living in close proximity to other religions, in order to maintain cohesion Judaism and Jews had to be very protective and even hostile to new ideas. And indeed to this day Jewish theology and preaching maintain a fairly dismissive attitude of other religions.
That being said Islam did have some notable impact on Judaism and Jewish theology when a prominent and eccentric Rabbi claiming to be the Messiah in 1666 converted to Islam after the Ottoman Sultan suggested this as the only alternative to losing his head - this did throw the Jewish theological world into a flux as he had quite a few followers and to this day Sabbateans (the self claimed prophet's name) is considered taboo among religious Jews.
Sources:
The Protestant Reformers and the Jews Excavating Contexts Unearthing Logic
G. Sujin Pak ,
Duke Divinity School, Durham.
Alice L. Eckardt
Maoz Kahana
Who Was Shabbetai Tsvi? False Messiah of the 17th century Jewish History Lecture Dr. Henry Abramson
(youtube lecture)