I have tried many variations like this, but none of them worked.
After few days, I found and tried this one that helped me.
So, I solved it by adding this code to my /android/app/src/main/AndroidManifest.xml:
<manifest>
...
<application>
...
<activity>
...
<intent-filter android:priority="999">
<action android:name="android.intent.action.VIEW" />
<category android:name="android.intent.category.DEFAULT" />
<category android:name="android.intent.category.BROWSABLE" />
<category android:name="android.intent.category.OPENABLE" />
<data android:host="*" />
<data android:mimeType="application/octet-stream" />
<data android:pathPattern=".*\\..*\\..*\\..*\\..*\\..*\\.YOUR_CUSTOM_EXTENSION" />
<data android:pathPattern=".*\\..*\\..*\\..*\\..*\\.YOUR_CUSTOM_EXTENSION" />
<data android:pathPattern=".*\\..*\\..*\\..*\\.YOUR_CUSTOM_EXTENSION" />
<data android:pathPattern=".*\\..*\\..*\\.YOUR_CUSTOM_EXTENSION" />
<data android:pathPattern=".*\\..*\\.YOUR_CUSTOM_EXTENSION" />
<data android:pathPattern=".*\\.YOUR_CUSTOM_EXTENSION" />
<data android:scheme="content" />
</intent-filter>
...
</activity>
</application>
</manifest>