Is adverse possession law still exist

Yes, adverse possession is still in effect in Kenya under the Limitations of Actions Act, Laws of Kenya. A person cannot sue to reclaim land after 12 years have passed since they first had the right to do so. This 12-year period starts either: When the person themselves first gained the right to claim the land, or when the person they inherited the right from first gained that right.
 

There are some conditions however which need to be fulfilled which are: the person claiming adverse possession must prove and demonstrate that he has occupied the land openly, that is without secrecy, without force, and without license or permission of the landowner, with the intention to have the land.

Yes, this doctrine is still in force and is grounded in Section 7 of the Limitation of Actions Act. 

Under this law, a person who has had continuous, open, and exclusive uninterrupted occupation and possession of the property over 12 years can move the court to facilitate his/her getting legitimate title to the land.

The concept applies to a trespasser who openly occupies the land without any secrecy or force with the intention of owning it.

The landowner, 'holder of the Certificate of Title/Lease,' must have been dispossessed or had discontinued possession of the property. This means the owner must have stopped physically using, managing, or asserting their rights over the property. However, the land owner must not have given permission or licensed the trespasser to occupy the land. Furthermore, despite the trespasser occupying the land, the land owner made no efforts to evict/collect rent from them within 12 years.

After 12 years have lapsed, the original owner loses the right to reclaim the land, and the 'trespasser' can apply to be registered as the owner under the doctrine of Adverse Possession.