what is the cost to replace the battery in my iphone 8SE?

Cost is $69 for an iPhone 8 Plus. I don't find a listing for an iPhone 8 SE.

Check Settings > Battery > Battery Health & Charging > Maximum Capacity

If the Maximum Capacity is less than 80%, the battery needs to be replaced.

Make an appointment at the Apple Store and they will often be able to replace the battery while you wait....30-45 minutes. But, no guarantees if the store is really busy when you arrive.

A better bet for fast service might be an authorized Apple Service shop. You don't need an appointment, and they will be a lot less busy. It took only about 15 minutes to replace the battery when I took my phone in to an authorized repair shop.....with no appointment.

The Apple Store here did not have appointments available for a few days last time I checked, but every store is different.

You can find an authorized service shop using this link: Find Locations

Are you sure you need a new battery?

See this excerpt from the "Your battery's maximum capacity" section of the support article: iPhone Battery and Performance - Apple Support

"A normal battery is designed to retain up to 80% of its original capacity at 500 complete charge cycles when operating under normal conditions. The one-year warranty includes service coverage for a defective battery. If it is out of warranty, Apple offers battery service for a charge." In other words, if maximum capacity is below 80%, the battery is below normal performance. You can still use a device with a lower health percentage than 80% but for optimal usage you may wish to consider having it changed when it reaches 80%.

Batteries are consumables and 1-2% loss per month is perfectly normal. According to iPhone Battery and Performance - Apple Support , Apple apparently only considers it unusual (and warrant-able) if a battery drops below 80% maximum capacity in less than a year after you receive it. Ergo, some storage loss as you use it is expected and acceptable. Incidentally, that possible 20% drop over the first 12 months equates to 1-2% drop per month being within the range of what Apple finds acceptable.

Go to this web site for information about how to request battery service for your iPhone: iPhone Battery Repair & Replacement - Apple Support

For cost and availability, enter your model information in the "Get an estimate" box at the bottom. (I will let you do this since the answer will depend upon the country where you are located.)

For instructions on how to get your iPhone, iPad, or iPod touch ready for service click here --> Get your iPhone, iPad, or iPod touch ready for service - Apple Support