Hi Prashant,

I have created a lightning component according to your requirements. Please try the below code:

Apex:

public class AccPicklistRelatedConC {
    
    @AuraEnabled
    public static List<Account> getAccountName() {
        List<Account> lstNames = [SELECT Id, Name FROM Account];
        return lstNames;
    }
    
    @AuraEnabled
    public static List<Contact> getConatct(String aName) {
        List<Contact> con = [SELECT Id, Name, Phone, Email, Account.Name FROM Contact WHERE Account.Name=:aName];
        return con;
    }
}

Component:

<aura:component controller="AccPicklistRelatedConC"
                implements="force:appHostable,flexipage:availableForAllPageTypes,flexipage:availableForRecordHome,force:hasRecordId,forceCommunity:availableForAllPageTypes,force:lightningQuickAction" access="global" >
    
    <aura:attribute name="PageHeading" type="String" default="Show Contact Records Related to Account"/>
    <aura:attribute name="pickName" type="List" />
    <aura:attribute name="picksel" type="String" />
    <aura:attribute name="mydata" type="Contact"/>
    <aura:attribute name="mycolumns" type="List"/>
    
    <aura:handler name="init" value="{!this}" action="{!c.doinit}"/>
    
    <div class="slds-m-top--xx-large">
        <div class="slds-page-header">
            <div class="slds-align--absolute-center">
                <div class="slds-text-heading--large">       
                    {!v.PageHeading}
                </div>
            </div>
        </div>
    </div>
    <br/> <br/>
    
    <div class = "slds-size--3-of-8">
        <lightning:select aura:id="selectid" label="Select Account Name" value="{!v.picksel}" onchange="{!c.onControllerFieldChange}" >
            <option value="" text="- None -" />
            <aura:iteration items="{!v.pickName}" var="pick">
                <option value="{!pick.Name}" text="{!pick.Name}" />
            </aura:iteration>
        </lightning:select>
        <br/><br/>
    </div>
    <br/><br/>
    
    <div class="slds-p-left_large slds-p-right_medium">
        
        <lightning:datatable data="{! v.mydata }" 
                             columns="{! v.mycolumns }" 
                             keyField="Id" 
                             hideCheckboxColumn="true"/>
    </div>
</aura:component>

Controller:

({
    doinit : function(component, event, helper) {
        component.set('v.mycolumns', [
            {label: 'Contact Name', fieldName: 'Name', type: 'text'},
            {label: 'Phone', fieldName: 'Phone', type: 'phone'},
            {label: 'Email', fieldName: 'Email', type: 'email'},
            {label: 'Account Name', fieldName: 'AccountName', type: 'text'}
        ]);
        
        var action = component.get("c.getAccountName");
        action.setCallback(this, function(response) {
            var state = response.getState();
            if (state === "SUCCESS") {
                var allValues = response.getReturnValue();
                console.log('allValues--->>> ' + JSON.stringify(allValues));
                component.set("v.pickName", allValues);
            }
            else if (state === "ERROR") {
                var errors = response.getError();
                if (errors) {
                    if (errors[0] && errors[0].message) {
                        console.log("Error message: " + 
                                    errors[0].message);
                    }
                } 
                else {
                    console.log("Unknown Error");
                }
            }
        });
        $A.enqueueAction(action);
    },
    
    onControllerFieldChange : function(component, event, helper){
        var pickselected = component.find("selectid").get("v.value");
        console.log('pickselected--->>> ' + pickselected);
        var action = component.get("c.getConatct");
        action.setParams({aName : pickselected});
        action.setCallback(this, function(response) {
            var state = response.getState();
            if (state === "SUCCESS") {
                var allValues = response.getReturnValue();
                console.log('allValues--->>> ' + JSON.stringify(allValues));
                for (var i = 0; i < allValues.length; i++) {
                    var row = allValues[i];
                    if (row.Account) row.AccountName = row.Account.Name;
                }
                component.set("v.mydata", allValues);
            }
            else if (state === "ERROR") {
                var errors = response.getError();
                if (errors) {
                    if (errors[0] && errors[0].message) {
                        console.log("Error message: " + 
                                    errors[0].message);
                    }
                } 
                else {
                    console.log("Unknown Error");
                }
            }
        });
        $A.enqueueAction(action);
    }
})

CSS:

.THIS {
}

.THIS.slds-size--3-of-8 {
    margin-left: 420px;
}

Application:

<aura:application extends="force:slds">
    <c:AccPicklistRelatedCon/>	
</aura:application>

I hope it helps you.

Kindly let me know if it helps you and close your query by marking it as solved so that it can help others in the future. It will help to keep this community clean.

Regards,
Khan Anas