Ideas to shop around
Directions rather than one particular thing, for when you’d rather choose. Some come with a few that fit.

Phone controllers
Turn a phone into a handheld console. Pick by phone type: Backbone has an iPhone and an Android version, GameSir X2 and Razer Kishi come in USB-C (Android and iPhone 15 and later) and Lightning versions. Check the phone before buying.
12 that fit · about $7.99 – $69.99
Backbone One (2nd Gen) Mobile Controller, USB-Cabout $69.99 · amazon.com
GameSir X5 Lite Mobile Controller (Android)about $29.99 · amazon.com
GameSir X2 Bluetooth Mobile Controllerabout $49.99 · amazon.com
Razer Kishi V3 Mobile Controllerabout $69.99 · amazon.com
8Bitdo Mobile Gaming Clip for Xbox Controllerabout $14.99 · amazon.com
OIVO PS5 Controller Phone Mount Clipabout $14.99 · amazon.com
Mocagen MC1 Phone Controllerabout $33.97 · amazon.com
AceGamer Aurora II Wireless Controllerabout $24.99 · amazon.com
8Bitdo Ultimate 2C Wireless Controllerabout $25.49 · amazon.com
arVin Mobile Gaming Controller for iPhone, Android and Tabletsabout $49.99 · amazon.com
Z108 Mobile Gaming Triggers (1 Pair)about $12.99 · amazon.com
Newseego Mobile Game Triggersabout $7.99 · amazon.com

Power and cooling
Long sessions drain the battery and heat up the phone, which slows the game down.
7 that fit · about $9.99 – $79.86
Anker Nano Power Bank 5Kabout $29.99 · amazon.com
Anker MagGo Power Bank 10Kabout $79.86 · amazon.com
CHONCHOW Magnetic Phone Cooler (RGB)about $12.34 · amazon.com
Black Shark FunCooler 5 Magnetic Phone Coolerabout $35 · amazon.com
CHONCHOW Magnetic Phone Coolerabout $12.99 · amazon.com
Black Shark FunCooler 5 Magnetic Phone Coolerabout $35 · amazon.com
Anker USB C to USB C Cable, 100W (2 Pack, 6 ft)about $9.99 · amazon.com

Grips and finger sleeves
Cheap upgrades for comfort and better touch control.
9 that fit · about $5.59 – $49.99
PopSockets Adhesive Phone Gripabout $9.94 · amazon.com
Mobile Gaming Finger Sleeves (10 pack)about $13.99 · amazon.com
Gaming Finger Sleeves (6 pack)about $8.59 · amazon.com
Gaming Finger Sleeves (20 pack)about $5.59 · amazon.com
RISOKA 10 Pieces Gaming Finger Sleevesabout $13.99 · amazon.com
20 PCS Gaming Finger Sleevesabout $5.99 · amazon.com
Soundcore by Anker Q20i Noise Cancelling Headphonesabout $49.99 · amazon.com
Nulaxy Aluminum Folding Phone Standabout $9.99 · amazon.com
MNN 15.6 inch Portable USB-C Monitorabout $43.81 · amazon.com

Game credits and subscriptions
Digital gifts that need no shipping: store credit, or a Game Pass subscription for cloud gaming on a phone.
3 that fit · about $15 – $68.99
Google Play Gift Codeabout $15 · amazon.com
Apple Gift Card (Email Delivery)about $25 · amazon.com
Xbox Game Pass Ultimate, 3 Month Membershipabout $68.99 · amazon.com