An image does not exist locally with the tag: while pushing image to local registry

You need to tag and push the image. When tagging an image, you can use the image identifier (imageId). It is listed when showing the list of all images with docker images. Syntax and an example (using imageId) for creating a tag are:

docker tag <imageId or imageName> <hostname>:<repository-port>/<image>:<tag>
docker tag af340544ed62 example.com:18444/hello-world:mytag

Once the tag, which can be equivalent to a version, is created successfully, you can confirm its creation with docker images and issue the push with the syntax:

docker push <hostname>:<repository-port>/<image>:<tag>

There is an example for local nexus repository

Successfully tagged user/apiserver:0.0.1

docker push localhost:5000/user/apiserver:0.0.1

Image tags need to include the registry name/port for you to push them anywhere other than the default registry (docker hub). So you need to tag your image as localhost:5000/user/apiserver:0.0.1 rather than user/apiserver:0.0.1. Then you'll be able to push to your local registry.