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Example script for damage type (execute on your player):
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const int DAMAGE_TYPE_PSYCHIC = 8192;

void main()
{
    SetTlkOverride(16877216, "Psychic Damage");
    SetTlkOverride(16877217, "<CUSTOM0> Psychic");
    
    effect eDamage = EffectDamage(DAMAGE_TYPE_PSYCHIC, 5);
    ApplyEffectToObject(DURATION_TYPE_INSTANT, eDamage, OBJECT_SELF);
}

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Test script for item property (excute on your player):
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const int IP_CONST_DAMAGETYPE_PSYCHIC = 15;

void main()
{
    SetTlkOverride(16877216, "Psychic Damage");
    SetTlkOverride(16877217, "<CUSTOM0> Psychic");
    SetTlkOverride(16877218, "Psychic");

    object oItem = GetItemInSlot(INVENTORY_SLOT_RIGHTHAND, OBJECT_SELF);
    if(GetIsObjectValid(oItem))
    {
        itemproperty ipAddDamage = ItemPropertyDamageBonus(IP_CONST_DAMAGETYPE_PSYCHIC, IP_CONST_DAMAGEBONUS_1d6);
        AddItemProperty(DURATION_TYPE_TEMPORARY, ipAddDamage, oItem, 60.0);
    }
}