The exception you are encountering (MQJCA1011) indicates that there was an internal error while attempting to allocate a JMS connection in the context of a message-driven bean (MDB). This could be due to various reasons, such as misconfiguration, connectivity issues, or other internal errors.

Without the specific details of your configuration and code, it’s challenging to provide an exact solution. However, I can provide you with a general outline and some common steps to troubleshoot and resolve such issues:

1. Verify MQ Connection Details:
2. Ensure that your MQ connection factory and destination details in the activation specification are correct.
3. Double-check the queue or topic names, host, port, and channel details.
4. Check Classpath and Dependencies:
5. Ensure that the necessary MQ JAR files are available in the classpath of your application.
6. Check for version compatibility between your WebSphere version and the MQ client library.
7. Logging and Tracing:
8. Enable detailed logging for the WebSphere Application Server and the MQ resource adapter to get more information about the failure.
9. Analyze logs to identify any specific error messages or stack traces.
10. Websphere MQ Configuration:
11. Verify the configuration of the WebSphere MQ resource adapter.
12. Check whether the activation specification is correctly associated with the appropriate connection factory.
13. Review Activation Specification Configuration:
14. Double-check the activation specification configuration in your ejb-jar.xml and ibm-ejb-jar-bnd.xmi.
15. Ensure that the mqJndiName property is set correctly.

Here is a simple example of configuring an activation specification in ejb-jar.xml:

<enterprise-beans>
    <message-driven>
        <ejb-name>YourMDB</ejb-name>
        <ejb-class>your.package.MdbListener</ejb-class>
        <activation-config>
            <activation-config-property>
                <activation-config-property-name>destination</activation-config-property-name>
                <activation-config-property-value>yourQueue</activation-config-property-value>
            </activation-config-property>
            <!-- Other activation-config-property elements as needed -->
        </activation-config>
    </message-driven>
</enterprise-beans>

Make sure that your ibm-ejb-jar-bnd.xmi is correctly configured to map the destination property to the corresponding JNDI name.

If the issue persists, considering the complexity, it might be beneficial to reach out to IBM support or consult the IBM WebSphere documentation for version-specific guidance. You may also want to check for any fix packs or updates for your WebSphere version that might address known issues related to JMS connections.