Intro
MGA seems to have had a Mubahila challenge with Abdul Haq, which started in 1891.  Ahmadiyya sources tell us that Abdul Haq Ghaznavi, a follower of Abdul Jabbar and a disciple of the famous Ahl-e-Hadith Imam Maulawi Abdullah Ghaznavi (1811–1881), began a Mubahila with MGA in 1891 over the topic of the death of Esa (As) (see Life of Ahmad by Dard, page 239).  The Muslims of India and the entire world believed that Jesus was sitting alive in the heavens in his physical body. He declared on the basis of his ‘revelations’ that MGA was an
infidel and that he would be thrown into hell because he claimed to be the like of Jesus (as). This Ishtihar was widely distributed by the followers of Abdul Jabbar, and MGA received a copy on February 9th, 1891.  So he wrote a letter to Maulawi Abdul Jabbar about the challenge, saying that he believed Abdul Haq to be a follower of his. In this letter MGA affirmed that he had claimed to be the Promised Messiah on the basis of direct revelation received from on high. He made it clear that Jesusas had died and could not come again. He admitted the possibility of the advent of other Messiahs also (see Life of Ahmad by Dard, page 239).  MGA
was prepared to enter into Mubahala if necessary though, according to his own belief, Mubahala was not necessary or permissible to settle minor differences of opinion amongst Muslims.  Anyhow, if eminent mullahs like Nadhir Husain of Delhi, Muhammad Husain of Batala and Ahmadullah of Amritsar signed a fatwa to the effect that Mubahala was permissible in such cases, then he would have no course left open but to go to Amritsar for the purpose
of the Mubahala and Abdul Haq must in that case bring with him his family and his friends, as required by the Holy Quran. This letter is dated February 11th, 1891, and was published in a supplement to the Riayd-e-Hind, Amritsar, dated March 15th, 1891, pages 1-4 (see Life of Ahmad by Dard, page 239–242).  In response to this Abdul Haq issued another Ishtihar: If Mubahala was not permissible amongst Muslims, why had MGA asked Maulawi Muhammad Ismael through the pages of his book, Fath-e-Islam, to hold a Mubahala with him?

27 May, 1893 in Amritsar
MGA agreed to have a Mubahila prayer in Amritsar.

1897
In Anjam-E-Athim, MGA writes: 

About Abdul Haq’s wife: 

“Ab Abdul Haq ko zaroor poochna chahiey ke uss ka wo mubahla ki barkat ka larka (boy) kahan gaya, kia andar hi andar pait me tahleel (disappear) pa gia ya phir rajaat qahqari(again) ker ke nutfa bun gia” (Roohani Khazain Volume 11, Page 311).  English translation is as follows, “Now ask Abdul Haq certainly about that Mubahila he had with me, where are the blessings of a boy, where did it go? Did he disappear ……”

“aur ab tak iss ( Abdul Haq ) ki aurat ke pait sei aik chooha bhi paida na hoa” (Roohani Khazain Volume 11, Page 311).  English translation is as follows, And until now, his wife hasn’t even given birth to a mouse.

1902
MGA writes Tuhfa’-e-Ghaznaviyya. It was printed (700 copies) at the Diya’ul Islam Press and
published in October 1902.

1907
MGA mentions Abdul Haq.

Links and Related Essays
https://ahmadiyyafactcheckblog.com/2017/11/28/mubahila-with-molvi-abdul-haq-ghaznavi-and-its-impact-on-mirza-qadiyani/

https://en.wikipedia.org/wiki/Abdullah_Ghaznavi