How I did it:-

Need to append or create a FactionShipStyleSetDefs.xml for your faction and change this line:-

    <InitialEscortFighter>FederationDefencePlatform</InitialEscortFighter>

Also need to add a ship class in this file:-

    <ShipClass>FederationDefencePlatform</ShipClass>

Then you need to add(or append) a Ship Class in ShipClassDefs.xml:-

    <!-- Begin Ship -->

    <ShipClass>
        <InternalName>FederationDefencePlatform</InternalName>
        <DisplayName>Defence Platform</DisplayName>
        <Description>Defence Platform</Description>
        <ThumbnailOverride>ALL_Defence_Platform_Hoplite_3D3C0765BB554662BEE108FF87B5FEB9.png</ThumbnailOverride>
        <ShipHullType>Small</ShipHullType>
        <ShipRule>Balanced</ShipRule>
        <ShipDesign>ALL_Defence_Platform_Hoplite_3D3C0765BB554662BEE108FF87B5FEB9</ShipDesign>
        <AIOnly>false</AIOnly>
        <AIShipClass>Defender</AIShipClass>
        <StrategicIcon>Guardian</StrategicIcon>
        <BlueprintDef>DefencePlatformBlueprint</BlueprintDef>
    </ShipClass>

Now you need to add(or append) too BluePrints.xml (or use an existing one):-

    <!-- Begin Blueprint -->

    <ShipBlueprint>
        <InternalName>DefencePlatformBlueprint</InternalName>
        <ShipHullType>Small</ShipHullType>
        <Role>Guardian</Role>
        <ShipGroup>Fighter</ShipGroup>
        <CanBeBuilt>false</CanBeBuilt>
        <RequiredComponentType>BeamWeapon</RequiredComponentType>
        <RequiredComponentType>KineticWeapon</RequiredComponentType>
        <RequiredComponentType>MissileWeapon</RequiredComponentType>
        <ComponentType>Shields</ComponentType>
        <ComponentType>PointDefense</ComponentType>
        <ComponentType>Armor</ComponentType>
        <ComponentType>BeamWeapon</ComponentType>
        <ComponentType>KineticWeapon</ComponentType>
        <ComponentType>MissileWeapon</ComponentType>
        <FillerComponentType>Shields</FillerComponentType>
        <FillerComponentType>PointDefense</FillerComponentType>
        <FillerComponentType>Armor</FillerComponentType>
        <FillerComponentType>BeamWeapon</FillerComponentType>
        <FillerComponentType>KineticWeapon</FillerComponentType>
        <FillerComponentType>MissileWeapon</FillerComponentType>
    </ShipBlueprint>
   

You have to first use EscortFighters effect before you can use EscortFightersCap like this:-

        <Stats>
            <EffectType>EscortFighters</EffectType>
            <Target>
                <TargetType>Starbase</TargetType>
            </Target>
            <BonusType>Flat</BonusType>
            <Value>3</Value>
        </Stats>

Then in another Component/Improvement/Module use the EscortFightersCap to increase the amount.

        <TargetType>Fleet</TargetType>

Change that to Shipyard or Ship?

You have me a bit paranoid that my escort fighter change is not actualy working now (I never did check in battle, mines a starbase module and just never attacked a AI with it active)

EDIT:-

I think the code should be:

<Mod>
      <EffectType>EscortFightersCap</EffectType>
      <Scope>Fleet</Scope>
      <Target>
        <TargetType>Ship</TargetType>
      </Target>
      <BonusType>Flat</BonusType>
      <Value>1</Value>
</Mod>

They just don't show up in combat.

Silly questions but, you are pointing at the right ShipDesign?

        <ShipClass>FederationDefencePlatform</ShipClass>

Did you add this too, in FactionShipStyleSetDefs.xml? I forgot to mention that in my initial reply to the OP (Apended my Inital reply with this info).