Ultimate Member customization. Change error message for the "E-mail Address" field in the Registration form.

custom_field_validation_user_email.php

<?php

/**
 * Custom validation and error message for the "E-mail Address" field.
 */
add_action( 'um_custom_field_validation_user_email_details', 'um_custom_validate_user_email_details', 999, 3 );
function um_custom_validate_user_email_details( $key, $array, $args ) {
	if ( $key == 'user_email' && isset( $args['user_email'] ) ) {
		if ( isset( UM()->form()->errors['user_email'] ) ) {
			unset( UM()->form()->errors['user_email'] );
		}
		if ( empty( $args['user_email'] ) ) {
			UM()->form()->add_error( 'user_email', __( 'E-mail Address is required', 'ultimate-member' ) );
		} elseif ( ! is_email( $args['user_email'] ) ) {
			UM()->form()->add_error( 'user_email', __( 'The email you entered is invalid', 'ultimate-member' ) );
		} elseif ( email_exists( $args['user_email'] ) ) {
			UM()->form()->add_error( 'user_email', __( 'The email you entered is already registered', 'ultimate-member' ) );
		}
	}
}

You can use the Custom Validation option to change the error message for the E-mail Address field in the Registration form. The custom_field_validation_user_email.php code snippet is an example for validation based on the Custom Validation option.

See articles Fields Validation and Custom validation email and error message in registration for details.

I got a problem with last elseif ( email_exists( $args['user_email'] ) ) I already has email in DB but got message - "The email you entered is invalid"

elseif ( ! is_email( $args['user_email'] ) ) {
UM()->form()->add_error( 'user_email', __( 'The email you entered is invalid', 'ultimate-member' ) );
}
not working