how to handle a web version of showdialog in C#

I am trying to accomplish a functionality from windows form in the web api MVC scenario.Clearly i am trying to execute code in a same Method between 2 different requests.Request 1 btnClick1 start the execution of the Method, send a change to Client to Open a child modal form .Wait for response from the child form(user will do input) Then the second request will send (from the child form) to execute the remaining piece of code. I don't know is there is a technology to do that today.

example: in windows forms you open a child form via form.ShowDialog()

public buttonClick(){

var x= 1+2;

ShowDialogChild();

===wait for response ==

ApplyOnParentForm(What is changed on child);

return to Parrent

}

=== form child clase

  ShowDialogChild(){ 

Do somthing() modified field that will be sent to parent }