Had to install osTicket recently, and it had bit of a problems with the ajax requests returning 404.
This config should be enough to get you started, you might not even need to change it, well besides the obvious things like server name and root.
Ideally it shouldn’t have if blocks, but I am too lazy right now to refine it.

server {
        root /var/www/osticket/;
        index index.php index.html;
        listen 80;

        server_name domain.com;

        set $path_info "";

        # Deny access to everything inside the include directory
        location ~ ^/include {
                deny all;
                return 403;
        }

        # Deny access to .htaccess
        location ~ /\.ht {
                deny all;
        }

        # Requests to /api/* need their PATH_INFO set, this does that
        if ($request_uri ~ "^/api(/[^\?]+)") {
                set $path_info $1;
        }

        # /api/*.* should be handled by /api/http.php if the requested file does not exist
        location ~ ^/api/(tickets|tasks)(.*)$ {
                try_files $uri $uri/ /api/http.php;
        }

        # /scp/ajax.php needs PATH_INFO too
        if ($request_uri ~ "^/scp/.*\.php(/[^\?]+)") {
                set $path_info $1;
        }

        # Catch requests to /scp/ajax.php/some/path and redirect them to ajax.php
        location ~ ^/scp/ajax.php/(.*)$ {
                try_files $uri $uri/ /scp/ajax.php;
        }

        # Set index.php as directory index
        location / {
                index index.php;
        }

        # PHP-FPM listening on 127.0.0.1:9001 or on a socket
        location ~ \.php$ {
                try_files $uri =404;
                fastcgi_pass 127.0.0.1:9001;
                #fastcgi_pass    unix:/var/run/php5-fpm.sock;
                fastcgi_index   index.php;
                fastcgi_param   SCRIPT_FILENAME         $document_root$fastcgi_script_name;
                fastcgi_param   PATH_INFO               $path_info;
                include fastcgi_params;
        }
}