Jerusalem is مقدسي Maqdisi. I am not sure about the others

Tripoli in Arabic is طرابلس. I don't see why طرابلسي couldn't be a valid nisba. That said, I'm not sure about Cairo and Jaffa either. Perhaps قاهري and يافي?

First of all, it is the doubled يّ with Shadda marker in standard Arabic (Fus-ha or MSA).. It is two يْي merged into one يّ producing a sound similar to 'Hi' or 'bye'..

A male-person from بَغْداد Baghdad is بَغْدادِيّ BAGH-DAA-DEYYE for a person affiliated to Baghdad.. and you simply add "the" to have الْبَغْدادِيّ THE-male-person from Baghdad..

A male person from عِراق Iraq is عِراقِيّ pronounced 3E-RAA-QEYYE for a person affiliated to Iraq.. and if you add "The", you'd get الْعِراقِيّ (THE-Iraqi)..

But there is a doubled ي in Nouns of Affiliation اسم نسب which is a chapter of Arabic grammar in standard Arabic (Fus-ha); however, the local dialect of non-standard Arabic often renders the double ي into a simple ي vowel: Baghdaadee بغدادي and 3eraaqi عراقي ..

However the correct grammar of standard Arabic is doubled يّ as in Baghdaadeyye بَغْدادِيّ and 3eraaqeyye عِراقِيّ ; with the feminine versions would be بَغْدادِيَّة and عِراقِيَّة ..

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The Nouns of Affiliation اسم النسب is a chapter of Arabic grammar of standard Arabic with rules and exceptions.. For the most parts, you just add the doubled يّ and remove the vowel and the ة at the end..

Cairo القاهِرَة >> affiliated to Cairo قاهِريّ (masculine) -- for example, a man from Cairo قاهِريّ or QAA-HE-REYYE

Egypt مِصْر >> Egyptian مِصْرِيّ ME9-REYYE (again masculine) -- but note that in non-standard Arabic, Egypt is spelled مَصْر MASR unlike in standard Arabic which is مِصْر MESR..

The Iraqi city of Kufa الكوفَة >> affiliated to Kufa كوفِيّ KOO-FEYYE -- for example, there is a particular font in Arabic that is affiliated to the city called الخط الكوفيّ (The Kufic font or the font from Kufa)..

Jaffa يافا >> affiliated to Jaffa يافِيّ YAA-FEYYE

Tripoli طَرابُلُسُ >> affiliated to Tripoli is 6A-RAA-BO-LO-SEYYE طَرابُلُسِيّ

France فَرَنْسا >> French FA-RAN-SEYYE فَرَنْسِيّ

Canada كَنَدا >> Canadian كَنَدِيّ

BUT THERE ARE EXCEPTIONS.. of which people SIMPLY DECIDED:

The Egyptian city of Tanta طَنْطا >> affiliated to Tanta طَنْطاوِيّ

Austria نَمْسا >> Austrian or affiliated to Austria نَمْساويّ

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Jerusalem has a common name الْقُدْس and a more formal/proper name بَيْت الْمَقْدِس.. So when make an affiliation name for الْقُدْس (Jerusalem), the Arabs would chose the more formal name بيت المقدس to produce the Affiliation Noun اسم النسب:

Jerusalem الْقُدْس >> affiliated to Jerusalem مَقْدِسِيّ or add "the" to have الْمَقْدِسِيّ

The reason WHY we do not say قُدْسِيّ is because قُدْسِيّ is a noun and an adjective meaning "divine" or "holy".. There is a rule that if the Noun of Affiliation produces something that can be interpreted as something else, then an alternative Noun should be used..

This-is a divine inspiration هَذَا إلهامٌ قُدْسِيّ - the word قُدْسِيّ is an adjective (a divine or a holy)..

This-is a-sort of (the) divine intervention هَذَا نَوْعٌ مِنَ التَّدْخُلِ الْقُدْسِيِّ -- Here, الْقُدْسِيِّ is an adjective "the divine" or "the holy", and it is NOT an affiliation noun to Jerusalem.. Therefore, according to the rules of Nouns of Affiliation, we should NOT consider قُدْسِيِّ or الْقُدْسِيِّ as nouns of affiliation to Jerusalem..

The alternate name is بَيْت الْمَقْدِس therefore, it was simply decided that مَقْدِسِيّ or الْمَقْدِسِيّ should be the Noun of Affiliation to Jerusalem..

قاهري يافاوي مقدسي طرابلسي