Garmin Model with Automatic Activity Tracking Like Google Timeline?

Check-out Garmin's Move IQ function: https://support.garmin.com/en-US/?faq=zgFpy8MShkArqAxCug5wC6

Most recent Fenix & Epix watches support it

Thanks,
Dose any Garmin watches record GPS in background that can be later fetch by a web API?

No, when an "activity" is recorded by MoveIQ then you see minimal data, the time it started, how long it was, what type (walk/run/...) and not much more. Maybe the distance, but certainly not the map, because GPS is not activated.

You can record an activity by manually starting it, then it records GPS as well.

Also note that this isn't the right forum for this topic (not that there is a much better one, but maybe chose some from here: https://forums.garmin.com/outdoor-recreation/)

Thanks
Is there any way to set some setting for GPS to be recorded like every 1 minutes

no, only either once per second, or "smart" mode, but even smart mode will probably be more than once per minute. Also it won't disable the GPS receiver so the battery consumption will be the same. If you would create your own app and run in the background then maybe you could enable the GPS every 5 minutes, get a fix, save it, but it would be not an easy task to do. And you would need to be a software engineer to do it.

If I activate smart mode
Can i read the GPS with web API?
and can it be  like real time tracking?

Yes, but that's probably not what you think Smart Mode means. It means you still need to manually start, stop the activity recording. Smart mode just saves data only when it changes, not every second. Think more like your heart rate or speed. When you're moving (actually even when you're not) the GPS coordinates will always change a little bit, so it doesn't have any meaning for that.

After you finish recording the app you can download it from the Garmin Connect website in some file formats that you can choose there.

Garmin watches have a LiveTrack feature that can automatically send position updates to a Garmin website (via your phone, so you need cellular coverage), and the link shared with your friends. However you first need to start an activity. 

If you need more battery life you can enable GPS UltraTrac mode, you get an up to 30% better battery life, but it records your position only every 10 to 60 seconds (instead of every second in normal mode).

There is also an Expedition mode (app), where position is recorded every hour (can be set between 15 to 90 min) but all other smart watch functions are disabled (no Bluetooth, no notification, no HR monitoring, no LiveTrack, etc...) . This is for multi-day tracking with no possibility to recharge your watch.

As noted by Flocsy, this is not the right forum, to discuss general watch usage, but app development issues.

To clarify, on most Garmin watches, Move IQ doesn’t record a full activity, it just puts an entry in your calendar like “Walking - 40 min”. The difference between that and a full activity is that a full activity typically enables GPS, records your location track, records HR more frequently (once per second), and collects other data.

On Venu, vivoactive, and vivosmart devices, Move IQ can actually automatically trigger recording of a full walk or run activity, based on the time threshold that you set in the Auto Activity Start settings.

Disclaimer: I’ve never seen this feature for myself, I only know what the support article says

Speaking of LiveTrack, the support article implies that LiveTrack works with Auto Activity Start.

https://support.garmin.com/en-CA/?faq=vV8trfTjiF9f3X9ninHZR8

This feature allows the watch to start an activity automatically when the Move IQ® auto activity detector feature detects you are walking or running. You can set the minimum time threshold for running to 1, 2, or 3 minutes and walking to 5, 10, or 15 minutes.

Activities will display in your activity history in your Garmin Connect account and will include the time leading up to the minimum threshold that has been set plus any continuous running or walking time detected after the minimum threshold. If you are using a GPS capable device and have GPS enabled for your walk and run activity profiles, your watch should default to using GPS when auto activity start is detected. 

NOTE: When you have Auto Activity Start enabled, the Extend LiveTrack feature in the Garmin Connect app cannot determine when the activity started; therefore, the ability to view it for up to 24 hours after it began is not possible.

What Are the Requirements for Auto Activity Start?

If you have a situation where a running or walking activity is not being recognized, ensure the following:

• Exercise must be a continuous walk or run that lasts at least the minimum threshold that has been set while wearing the watch.

• Move IQ and Auto Activity Start are both enabled in Garmin Connect