The Google Chromecast (2013) is well known for its budget price and ability to wirelessly display YouTube and other Apps from Android smartphones like the Redmi Note 3 on to Smart TVs like the Samsung K4300 Joy Smart TV.
To use Google Chromecast (2013), make sure that you have connected the Chromecast to one of the HDMI ports of the TV and powered on the Chromecast by attaching the USB cable to a TV USB port or a USB power adapter. You also need to make sure your TV is powered up, and the HDMI input of your TV is the same port that you connected the Chromecast to.
From your Redmi Note 3, download and install the Google Home App from the Google Play Store.
Open the App and select the top right menu icon -> Cast screen / audio -> CAST SCREEN / AUDIO. The App will then search for the Google Chromecast (2013). You can select your Google Chromecast (2013) model once it is found, and the casting connection process will start.
Once the casting connection is established, you should be able to view the Redmi Note 3's screen on the TV connected to the Google Chromecast (2013). Despite having the Chromecast (2015) as its successor, the Google Chromecast (2013) is still well received due its low price and ability to support a wide range of Android smartphones.