Welcome to YT ! You are required by Law in the state of California to try Publicly to find a dogs owner as animals are considered property. You can run an add for a Found dog in the lost/found section of your local newspaper, FYI you can run a Found add for free Because the Law requires it
. Also you can call around to some Local shelters & tell them you have the dog, give a description & your Phone #, tell them you will keep the dog till the owner calls & if the owner doesn't call within the required by law time then legally the dog is considered yours. Also when you run the add in the newspaper Only say that you have found a very small dog & please call to identify or every one will be calling trying to get a free yorkie.