So I want to  make a homebrew armor wich gives cold resistance and gives bonus AC according to Strength and Constitution modifiers. But somehow I can't remove the basic Dex modifier. Is there a way to do so?

Yes. First, add the following Modifier:

• Modifier: Set->Subtype: AC Max Dex Armored Modifier->Fixed Value: 0

Then, Under Basic Information you have to set “Dex Bonus” to 0 and [SAVE CHANGES].

I tried but it didn't help. When I equip the armor it still gives the max 2 dex modifier to my AC. 

Did that character already have the armor in inventory before you changed how the armor was set up?

Did you set the armor to require attunement? If so, did you attune it to your character, or just equip it?

The character had that in the inventory however I deleted from his inventory and refreshed it. The armor was not set to require attunement. Also if I add a minus 2 modifier to the armor it is working instantly, but the dex modifier won't go away. 

Hmm…. Strange.

I tried pretty much everything. Adding more modifiers to ignore Dex, recreating the whole item with new armor, still +2 Dex to AC just sticks there.

Is your BASE ITEM TYPE armor or item? If you pick armor, you cannot eliminate the DEX bonus. Nothing will eliminate the DEX bonus. If you pick item, you can set it up to apply the modifiers correctly.

From my thread How to replace DEX in AC:

From Mordenkainen's Codex of Allies' Arcane Tradition Invention:

Starting at 2nd level, you gain proficiency with light armor and gain a suit of alchemical armor— a magic item that only you can attune to. While you are attuned to it and wearing it, it grants you resistance to force damage and you can use the armor as a spellcasting focus by extending one of your hands, so long as that hand is free.

The armor is light armor and provides an AC of 11 + your Intelligence modifier. It weighs 8 pounds.

We can reproduce this in a homebrew magic item:

RARITY: Whatever you want. The more rare, the further up in your inventory it'll show up
BASE ITEM TYPE: Item
MAGIC ITEM TYPE: Wondrous Item
REQUIRES ATTUNEMENT: Checked
ATTUNEMENT DESCRIPTION: by a Wizard in the Arcane Tradition of Invention

We have to make this an Item instead of Armor because Armor adds DEX to your AC no matter what

Modifiers:

MODIFIER TYPE:Resistance
MODIFIER SUBTYPE: Force

MODIFIER TYPE: Set
MODIFIER SUBTYPE: AC Max Dex Modifier
FIXED VALUE: 0

MODIFIER TYPE: Bonus 
MODIFIER SUBTYPE: Armor Class
FIXED VALUE: 1

MODIFIER TYPE: Bonus 
MODIFIER SUBTYPE: Armor Class
PRIMARY STAT: INT

 Resistance Force is there because of the text. It is not important for what this thread is about

1. First you have to set the AC Max DEX Modifier to 0
2. Second you have to set the base AC for the item. Dndbeyond already says your AC is 10 plus stuff. For this magic item we want 11 + stuff. Subtract 10 from what you want the new base to be and use that number here as a Bonus to Armor Class. In this case we're adding 1
3. Third you need to add a bonus to your AC using your INT modifier.

Equip and attune this item and BAM, your AC is now 11 + your INT modifier.