Assalamualaikum

مَّٰكِثِينَ فِيهِ أَبَدًا

Surah Kahf 18:3

مَّٰكِثِينَ :

This is an Ism with ending combination (eena) -

1. Status - Nasb or Jarr 
2. Number - 3 or more
3. Gender - No sign of feminine so masculine
4. Type - Common

Root Letters are م ك ث

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This word follows pattern of Mujarrad Family Sarf - Family 1 ( with no extra letters other than root letters in فعل ماضي )

مَكَثَ يَمْكُثُ مَكْثً …

Following pattern of باب نَصَرَ

Singular version of مَّٰكِثِينَ is مَاكِثٌ

مَاكِثٌ - is Ism Fa’il ( اسم فاعل - one who does the action ) that we get in doing sarf of مَكَثَ

فِيهِ

فِيهِ is Jarr Majroor Fragment فِي is Harf Jarr and هُ Majroor ( Rafa version is هُوَ ) ه has Kasra ( ِ ) because it comes after ي (for better pronounciation)

أَبَدًا

أَبَدًا is Ism

1. Status - Nasb 
2. Number - 1 Singular
3. gender - Masculine
4. Type - Common

Analyzing the sentence :

مَّٰكِثِينَ could be Mansoob or Majroor

For it to be Majroor there should be Harf Jarr before it or it should be Mudhaf Ilay. But since neither of these conditions match so it is not Majroor.

So مَّٰكِثِينَ should be Majroor now lets find out the reason for it to be Mansoob

Here مَّٰكِثِينَ is Haal of هُم ( of لهم ) in the previous Ayah. ( أَنَّ لَهُمْ أَجْرًا حَسَنًا … )

We looked into Haal in Part 3 blog of Surah Kahf - please refer to it Link

هم is صاحب الحال ( thing مَّٰكِثِينَ is describing )

Haal and Sahibul haal matches in gender and number

فِيهِ Jaar Majroor - متعلقان بـماكثين

أَبَدًا is ظرف متعلق بـماكثين

Translation of Ayah :

in which they will remain forever;