To create child record with Parent record information using Quick Action in Salesforce, we can use

1. force:recordData to get Parent record information

2. e.force:createRecord to create child record

Sample Code:

Lightning Aura Component:

<aura:component implements="force:hasRecordId,force:lightningQuickActionWithoutHeader" >
    <aura:attribute name="caseRecordError" type="String"/>
    <aura:attribute name="recordFields" type="Object" />
    <force:recordData 
                      recordId="{!v.recordId}"
                      aura:id="caseRecordCreator"
                      targetFields ="{!v.recordFields}"
                      targetError="{!v.caseRecordError}"
                      layoutType="FULL"
                      fields="Id,Name"   
                      recordUpdated="{!c.handleRecordUpdated}" 
                      />
</aura:component>

Lightning Aura Component JavaScript Controller:

({
    
    handleRecordUpdated : function(component, event, helper) {
        
        let closeActionPanel = $A.get( "e.force:closeQuickAction" );
        closeActionPanel.fire();
        let createCaseFromAccount = $A.get( "e.force:createRecord" );
        let accountRec = component.get( "v.recordFields" );     
        let accountId = component.get( "v.recordId" );
        let caseInternalRecTypId = $A.get( "$Label.c.CaseInternalRecordType" );
        console.log( 'caseInternalRecTypId is', caseInternalRecTypId );
        
        createCaseFromAccount.setParams( {
            "entityApiName": "Case",
            "defaultFieldValues": {
                'AccountId' : accountId,
                'Subject' : accountRec.Name + ' Case'
            },
            "recordTypeId" : caseInternalRecTypId
        } );
        createCaseFromAccount.fire();
        
    }
    
} )

Quick Action:

Output: