As a student of medicine, I seldom find time for exercise. By the grace of God, I pray regularly in the mosque. To get some exercise, I normally jog to the mosque. Now, I came across this Hadīth which says that one must not run to the mosque. Should I stop then?

Your situation is totally different from the one depicted in the Hadīth. It says that when a person is going to offer congregational prayers in a mosque, he should walk in a composed fashion. Abū Hurayrah reports that he heard the Prophet saying:

When the congregational prayer is about to commence, do not rush to join it; walk towards it. It is imperative that you maintain your calm [in this matter]. Pray whatever [number of Rak‘ats] you are able to catch and then complete the rest. If any one of you has made up his mind to pray, then he has in fact started to pray. (Muslim, Kitābu’l-Masājid)

It is evident from this narrative that worship rituals should be observed with full composure. It is a matter of etiquette. Moreover, rushing into the prayer not only affects the person’s concentration but also disturbs the other participants. Also, the last part of the narrative gives the glad tidings that a person who is planning to pray is in fact praying. So why should he rush at all if he is in fact getting the reward of praying.

In my opinion, jogging to the mosque to get exercise does not contradict this Hadīth. It is quite obvious that you are not jogging to the mosque for fear of getting late. Moreover, once you reach the mosque gate, you should walk calmly to the actual prayer place so that you do not cause any undue noise.