To do as you described, create a Maven project with packaging maven-plugin. In the src/main/resources/META-INF/plexus sub-folder create a components.xml with the following contents (assuming you want the packaging type to be "my-custom-type", change it to "foobar" if you wish).
<component-set>
<components>
<component>
<role>org.apache.maven.lifecycle.mapping.LifecycleMapping</role>
<role-hint>my-custom-type</role-hint>
<implementation>
org.apache.maven.lifecycle.mapping.DefaultLifecycleMapping
</implementation>
<configuration>
<phases>
<!--use the basic jar lifecycle bindings, add additional
executions in here if you want anything extra to be run-->
<process-resources>
org.apache.maven.plugins:maven-resources-plugin:resources
</process-resources>
<package>
org.apache.maven.plugins:maven-jar-plugin:jar
</package>
<install>
org.apache.maven.plugins:maven-install-plugin:install
</install>
<deploy>
org.apache.maven.plugins:maven-deploy-plugin:deploy
</deploy>
</phases>
</configuration>
</component>
<component>
<role>org.apache.maven.artifact.handler.ArtifactHandler</role>
<role-hint>my-custom-type</role-hint>
<implementation>
org.apache.maven.artifact.handler.DefaultArtifactHandler
</implementation>
<configuration>
<!--the extension used by Maven in the repository-->
<extension>foobar</extension>
<!--the type used when specifying dependencies etc.-->
<type>my-custom-type</type>
<!--the packaging used when declaring an implementation of
the packaging-->
<packaging>my-custom-type</packaging>
</configuration>
</component>
</components>
</component-set>
Then in a pom that is to have the custom packaging, declare the required type in the packaging element, and ensure you have specified the plugin so the custom packaging can be contributed. Declaring <extensions>true</extensions> tells Maven that the plugin contributes packaging and/or type handlers to Maven.
<project
xmlns="http://maven.apache.org/POM/4.0.0"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
xsi:schemaLocation="http://maven.apache.org/POM/4.0.0
http://maven.apache.org/maven-v4_0_0.xsd">
<modelVersion>4.0.0</modelVersion>
<groupId>name.seller.rich</groupId>
<artifactId>test</artifactId>
<version>0.0.1-SNAPSHOT</version>
<packaging>my-custom-type</packaging>
<build>
<plugins>
<plugin>
<groupId>name.seller.rich.maven.plugins</groupId>
<artifactId>maven-foobar-plugin</artifactId>
<version>0.0.1</version>
<!--declare that this plugin contributes the component extensions-->
<extensions>true</extensions>
</plugin>
</plugins>
</build>
</project>
When the project is packaged, it will be a jar, with a .jar extension, however when it is installed/deployed, Maven will deliver the file to the repository with the ".foobar" extension as specified in components.xml