Wikipedia says that when Constantinople fell and the Hagia Sophia was converted to a mosque, the mosiacs depicting Jesus were either covered or destroyed. Since Muslims believe in Jesus, why were these mosaics covered or destroyed?

Well the thing is, that during the first centuries of Hagia Sophia's history as a Mosque the mosaics were infact uncovered and were still prominently on display. When Cornelius Loos made his engravings of Constantinople around 1710, he documented the mosaics pretty clearly (this example is particularily striking as it shows the Virgin Mary, still prominent over the Islamic Mihrab). Some of his engravings even show mosaics that have now been completely lost.

Shortly after Loos made these engravings, the mosaics of the mosque were covered up and replaced with white plaster. We don't know for sure when this happened as there is no official proclaimation, but the interior of the Hagia Sophia was renovated in 1717, so it is quite possible that this is when the mosaics were covered up, just 17 years after Loos made his drawings.

So what took the Ottomans so long, and why did they make the decision to cover these mosaics up by almost 400 years after they took the city? There were several renovations to the Hagia Sophia after the conquest, so why did they not cover them up?

The preservation of the mosaics seem to have been an intentional choice. For example, the windows, altar, bell tower and Patriarchate of the Hagia Sophia were all destroyed or replaced. The Ottoman Sultans could have easily also destroyed the mosaics or covered them up, but they didn't for whatever reason. Here are a few theories I have heard for why the mosaics may have been preserved and later covered up:

It may be that these mosaics were preserved to serve as trophies of the conquest. The Hagia Sophia was itself preserved partially for this reason. The presence of the mosaics next to the Islamic calligraphy and Mihrab would remind the visitor of what used to be, and clearly signal the appropriation and reconversion of this former church.

Another theory might be that the Ottomans, despite being Muslim, wanted to emphasize some degree of continuity, or respect with the past. That these mosaics were to be admired for their beauty rather than for their religious significance, and give the Ottoman Sultans legitimacy as protectors and successors of the Roman imperial past. Mehmed II did proclaim himself Caesar of Rome after all, and specifically decided to have the Hagia Sophia converted from Imperial Church to Imperial Mosque to bolster this claim.

But if any of these were the case, why were these mosaics later covered up? Well for one, the Ottoman Empire in 1717 was in a very different place compared to earlier centuries. Ottoman Sultans no longer really took their claims as Caesar of Rome seriously (After Suleiman the title seems to have faded into obscurity). The Ottomans were also slowly being encroached by the Habsburg and Russian Empire to its north and west. The Empire would manage to survive this encroachment, but the sudden losses to Christian states may have provoked a defensive attitude among some Ottomans, which may have made these Christian mosaics in the Imperial Mosque somewhat uncomfortable. Several other former churches in Constantinople, like the Zeyrek Mosque and the Little Hagia Sophia also had their mosaics covered in plaster during the 18th Century aswell. Which implies that it may have been a larger ideological change that caused this.

It is also important to point out that by the 18th Century these mosaics were in very poor condition and were probably falling apart. Some of the broken tesserae from the mosaics were even stolen by local salesmen, who would sell them as "gemstones". So the mosaics may simply have been covered up because they were falling apart, which accidentally saved many of them and allowed them to be uncovered much later.

It is tempting to want to look for theological reasons for why the mosaics were covered up. But it becomes difficult to reconcile such arguments with the nearly 400-year long preservation of the mosaics in the mosque.

I hope this answered your question in a satisfactory manner. If you want me to elaborate more, just ask.