How To give notifications on android on specific time?

You can use AlarmManager to set alarm at specified time

SharedPreferences prefs = PreferenceManager.getDefaultSharedPreferences(this);
if (!prefs.getBoolean("firstTime", false)) {

    Intent alarmIntent = new Intent(this, AlarmReceiver.class);
    PendingIntent pendingIntent = PendingIntent.getBroadcast(this, 0, alarmIntent, 0);

    AlarmManager manager = (AlarmManager) getSystemService(Context.ALARM_SERVICE);

    Calendar calendar = Calendar.getInstance();
    calendar.setTimeInMillis(System.currentTimeMillis());
    calendar.set(Calendar.HOUR_OF_DAY, 7);
    calendar.set(Calendar.MINUTE, 0);
    calendar.set(Calendar.SECOND, 1);

    manager.setRepeating(AlarmManager.RTC_WAKEUP, calendar.getTimeInMillis(),
            AlarmManager.INTERVAL_DAY, pendingIntent);

    SharedPreferences.Editor editor = prefs.edit();
    editor.putBoolean("firstTime", true);
    editor.apply();
}

I used SharedPreferences to check that's not the first time to run the app and if it is, you set that alarm otherwise do nothing instead of resetting the alarm each time you start your app.
Use a BroadcastReceiver to listen when the alarm happens

public class AlarmReceiver extends BroadcastReceiver {
    @Override
    public void onReceive(Context context, Intent intent) {
        // show toast
        Toast.makeText(context, "Alarm running", Toast.LENGTH_SHORT).show();
    }
}

Use another receiver to listen to device boots so that you can reset the alarm

public class DeviceBootReceiver extends BroadcastReceiver {
    @Override
    public void onReceive(Context context, Intent intent) {
        if (intent.getAction().equals("android.intent.action.BOOT_COMPLETED")) {
            // on device boot compelete, reset the alarm
            Intent alarmIntent = new Intent(context, AlarmReceiver.class);
            PendingIntent pendingIntent = PendingIntent.getBroadcast(context, 0, alarmIntent, 0);

            AlarmManager manager = (AlarmManager) context.getSystemService(Context.ALARM_SERVICE);

            Calendar calendar = Calendar.getInstance();
            calendar.setTimeInMillis(System.currentTimeMillis());
            calendar.set(Calendar.HOUR_OF_DAY, 7);
            calendar.set(Calendar.MINUTE, 0);
            calendar.set(Calendar.SECOND, 1);

            manager.setRepeating(AlarmManager.RTC_WAKEUP, calendar.getTimeInMillis(),
                    AlarmManager.INTERVAL_DAY, pendingIntent);
        }
    }
}

add the permission to the manifest

<uses-permission android:name="android.permission.WAKE_LOCK" />
<uses-permission android:name="android.permission.RECEIVE_BOOT_COMPLETED" />

then register your receivers

<receiver android:name=".DeviceBootReceiver">
    <intent-filter>
        <action android:name="android.intent.action.BOOT_COMPLETED" />
    </intent-filter>
</receiver>
<receiver android:name=".AlarmReceiver" />

A solution from the accepted answer will not work properly on Android 8 Oreo (api level 26) and higher due to background service limits (https://developer.android.com/about/versions/oreo/background.html#services) and will cause an exception like this when the app is in background:

java.lang.IllegalStateException: Not allowed to start service Intent xxx: app is in background

One of the possible workarounds is using JobIntentService:

1. extend your Service from JobIntentService instead of IntentService and use onHandleWork method instead of onHandleIntent.

2. add android:permission="android.permission.BIND_JOB_SERVICE" to your Service in AndroidManifest.xml.

first you need to use a broadcastreceiver. and because a broadcast receiver up only for a short time

from the android developer blog.When handling a broadcast, the application is given a fixed set of time (currently 10 seconds) in which to do its work. If it doesn't complete in that time, the application is considered to be misbehaving, and its process immediately tossed into the background state to be killed for memory if needed.

its a better practice to use also intent service here you have a example how to do it.

this is the broadcast receiver class.

public class MyReceiver extends BroadcastReceiver {
    public MyReceiver() {
    }

    @Override
    public void onReceive(Context context, Intent intent) {

        Intent intent1 = new Intent(context, MyNewIntentService.class);
        context.startService(intent1);
    }
}

and register it in the manifest.

<receiver
    android:name=".MyReceiver"
    android:enabled="true"
    android:exported="false" >
</receiver>

this is the intent service class.

public class MyNewIntentService extends IntentService {
    private static final int NOTIFICATION_ID = 3;

    public MyNewIntentService() {
        super("MyNewIntentService");
    }

    @Override
    protected void onHandleIntent(Intent intent) {
        Notification.Builder builder = new Notification.Builder(this);
            builder.setContentTitle("My Title");
            builder.setContentText("This is the Body");
            builder.setSmallIcon(R.drawable.whatever);
        Intent notifyIntent = new Intent(this, MainActivity.class);
        PendingIntent pendingIntent = PendingIntent.getActivity(this, 2, notifyIntent, PendingIntent.FLAG_UPDATE_CURRENT);
        //to be able to launch your activity from the notification 
        builder.setContentIntent(pendingIntent);
        Notification notificationCompat = builder.build();
        NotificationManagerCompat managerCompat = NotificationManagerCompat.from(this);
        managerCompat.notify(NOTIFICATION_ID, notificationCompat);
    }
}

and register it in the manifest.

<service
    android:name=".MyNewIntentService"
    android:exported="false" >
</service>

and then in your activity set the alarm manger to start the broadcast receiver at a specific time and use AlarmManager setRepeating method to repeat it this example bellow will repeat it every day.

 Intent notifyIntent = new Intent(this,MyReceiver.class);
PendingIntent pendingIntent = PendingIntent.getBroadcast
            (context, NOTIFICATION_REMINDER_NIGHT, notifyIntent, PendingIntent.FLAG_UPDATE_CURRENT);
AlarmManager alarmManager = (AlarmManager) context.getSystemService(Context.ALARM_SERVICE);
alarmManager.setRepeating(AlarmManager.RTC_WAKEUP,  System.currentTimeMillis(),
            1000 * 60 * 60 * 24, pendingIntent);

i hope this will help you.