What do you get for winning a Seize Peripheral Duchy war in CK3?

The attacker gains the contested Title (patch 1.20.0.3).

What does the Seize Peripheral Duchy casus belli cost?

piety and prestige; the amount depends on the titles, claims and distance, worked out when you declare.

Casus belli · Conquest

Seize Peripheral Duchy

Seize Peripheral Duchy is a casus belli in Crusader Kings III (conquest). If the attacker wins: The attacker gains the contested Title. If the defender wins: The defender keeps the contested Title. Declaring it costs piety and prestige. The war goal is worth 50% war score. Patch 1.20.0.3, from game/common/casus_belli_types/07_ep3_wars.txt.

Quick answers (3)

What do you get for winning a Seize Peripheral Duchy war in CK3?: The attacker gains the contested Title (patch 1.20.0.3).
What happens on a white peace?: The defender keeps the contested Title.
What does the Seize Peripheral Duchy casus belli cost?: piety and prestige; the amount depends on the titles, claims and distance, worked out when you declare.

How the war ends

Attacker wins

The attacker gains the contested Title.

White peace

The defender keeps the contested Title.

Defender wins

The defender keeps the contested Title.

If the war becomes invalid

The … has ended: the defender no longer … any land in the target region.

Who can declare it

The game shows no text of its own for these conditions; the script is below.

Every conquest war (the group's allowed_for_character) (7 lines of game script)

herders_and_tributary_constraints = yes
pam_personal_pacifism_offensive_war_ban_trigger = yes
tgp_dynastic_cycle_offensive_wars_ban_trigger = yes
tgp_war_ban_all_ministers_trigger = yes
NOT = {
	government_has_flag = government_is_theocracy
}

As written in game/common/casus_belli_groups/00_casus_belli_groups.txt.

Attacker (allowed_for_character) (4 lines of game script)

NOT = {
	government_has_flag = government_is_landless_adventurer
}
is_landed = yes

As written in game/common/casus_belli_types/07_ep3_wars.txt.

Defender (allowed_against_character) (9 lines of game script)

scope:defender = {
	government_has_mechanic = administrative
}
scope:attacker = {
	ALL_FALSE = {
		top_liege = scope:defender.top_liege
		liege = scope:defender
	}
}

As written in game/common/casus_belli_types/07_ep3_wars.txt.

When it can start (valid_to_start) (26 lines of game script)

scope:target = {
	any_in_de_jure_hierarchy = {
		tier = tier_county
		OR = {
			is_coastal_county = yes
			any_neighboring_county = {
				holder = {
					target_is_same_character_or_above = root
				}
			}
		}
	}
	this != scope:defender.top_liege.capital_county.duchy
	trigger_if = {
		limit = {
			scope:defender.top_liege.primary_title.tier >= tier_empire
		}
		empire != scope:defender.top_liege.capital_county.empire
	}
	trigger_if = {
		limit = {
			scope:defender.top_liege.primary_title.tier = tier_kingdom
		}
		kingdom != scope:defender.top_liege.primary_title
	}
}

As written in game/common/casus_belli_types/07_ep3_wars.txt.

Cost to declare

Costs piety and prestige. The amount is worked out when you declare (by the titles targeted, claims, distance and more), so the script is shown as written:

Cost (21 lines of game script)

piety = {
	value = 0
	add = common_cb_impious_piety_cost
}
prestige = {
	value = 0
	add = {
		every_in_list = {
			list = target_titles
			every_in_de_jure_hierarchy = {
				limit = {
					tier = tier_county
					holder.top_liege = scope:defender
				}
				add = 50
			}
		}
		desc = CB_CLAIM_COST_TARGET_TITLES
	}
	multiply = common_cb_prestige_cost_multiplier
}

As written in game/common/casus_belli_types/07_ep3_wars.txt.

Source: game/common/casus_belli_types/07_ep3_wars.txt and the English localisation, Crusader Kings III 1.20.0.3. “The attacker”, “the defender” stand where the game names the character; “…” marks other words it fills in during play.