Hi Babu,
Please take following code as reference:
$(document).ready(function() {
// Add event validator
if (typeof(Page_Validators) == 'undefined') return;
// Create new validator
var newValidator = document.createElement('span');
newValidator.style.display = "none";
newValidator.id = "emailaddress1Validator";
newValidator.controltovalidate = "emailaddress1";
newValidator.errormessage = "Email is a required field.";
newValidator.evaluationfunction = function() {
if (!$('#new_acceptance_0').is(':checked') && $('#new_acceptance_1').is(':checked')) {
if ($('#emailaddress1').val() == "") {
return false;
} else {
return true;
}
} else {
return true;
}
};
Page_Validators.push(newValidator);
// Add validator element
$("#new_acceptance_0").change(function() {
if (this.checked) {
$("#emailaddress1").attr('aria-required', "false");
$('#emailaddress1').parent().prev().removeClass("required");
}
});
$("#new_acceptance_1").change(function() {
if (this.checked) {
$("#emailaddress1").attr('aria-required', "true");
$('#emailaddress1').parent().prev().addClass("required");
}
});
})
It consists of two part:
1. Create a logic validator(newValidator variable) to prevent submit event and throw error message when specific condition meets.
2. Create an element validator, if specific condition meets, add "required" class to parent label of field.
e.g:
If Acceptance field equals "Yes", then set Email field to be mandatory.
1. By default:

2. When "Yes" button is checked, add red "*" character to Email label.
(If switch to "No", the element will be removed.)

3. Error message will appear if "Acceptance" equals "Yes" and Email field is empty.

Core logic: return false if
-> radio button 1 is not checked and radio button 2 is checked
->> if email field is emplty
The article below introduced how to add custom validator.
https://docs.microsoft.com/en-us/powerapps/maker/portals/configure/add-custom-javascript
Regards,
Clofly