As you have not provided your entire route setup. This answer is my best guess. See if it helps.
Your issue hint at improper route setup. If you have created a clinic resource then clinic/register route should precede it.
// clinic/register route should come first
Route::get('clinic/register','ClinicController@register');
// followed by rest of the routes which resource will create
Route::resource('clinic','ClinicController');
The reason behind getting a blank pages is because Route::resource will create some route with wildcards.
For e.g. clinic/{clinic} which will map to show method on controller. So when you make a get request to clinic/register it will be mapped to this show method instead of your register method.
One possibility for not getting any errors is your show method does not have any code yet. Hence, a blank response.
To summarize: Order in which you register your routes matters
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