Solution 1:

You can refer to my working sample code. Hope this helps!

public class MainActivity extends AppCompatActivity {

    private TextView mTextView;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        mTextView = (TextView) findViewById(R.id.textView);

        String url = "https://192.168.1.100/testvolley";

        HurlStack hurlStack = new HurlStack() {
            @Override
            protected HttpURLConnection createConnection(URL url) throws IOException {
                HttpsURLConnection httpsURLConnection = (HttpsURLConnection) super.createConnection(url);
                try {
                    httpsURLConnection.setSSLSocketFactory(getSSLSocketFactory());
                    httpsURLConnection.setHostnameVerifier(getHostnameVerifier());
                } catch (Exception e) {
                    e.printStackTrace();
                }
                return httpsURLConnection;
            }
        };

        final JsonObjectRequest jsonObjectRequest = new JsonObjectRequest(Request.Method.GET, url, new Response.Listener<JSONObject>() {
            @Override
            public void onResponse(JSONObject response) {
                try {
                    mTextView.setText(response.toString(5));
                } catch (JSONException e) {
                    mTextView.setText(e.toString());
                }
            }
        }, new Response.ErrorListener() {
            @Override
            public void onErrorResponse(VolleyError error) {
                mTextView.setText(error.toString());
            }
        });

        final RequestQueue requestQueue = Volley.newRequestQueue(this, hurlStack);

        requestQueue.add(jsonObjectRequest);
    }

    // Let's assume your server app is hosting inside a server machine
    // which has a server certificate in which "Issued to" is "localhost",for example.
    // Then, inside verify method you can verify "localhost". 
    // If not, you can temporarily return true
    private HostnameVerifier getHostnameVerifier() {
        return new HostnameVerifier() {
            @Override
            public boolean verify(String hostname, SSLSession session) {
                //return true; // verify always returns true, which could cause insecure network traffic due to trusting TLS/SSL server certificates for wrong hostnames
                HostnameVerifier hv = HttpsURLConnection.getDefaultHostnameVerifier();
                return hv.verify("localhost", session);
            }
        };
    }

    private TrustManager[] getWrappedTrustManagers(TrustManager[] trustManagers) {
        final X509TrustManager originalTrustManager = (X509TrustManager) trustManagers[0];
        return new TrustManager[]{
                new X509TrustManager() {
                    public X509Certificate[] getAcceptedIssuers() {
                        return originalTrustManager.getAcceptedIssuers();
                    }

                    public void checkClientTrusted(X509Certificate[] certs, String authType) {
                        try {
                            if (certs != null && certs.length > 0){
                                certs[0].checkValidity();
                            } else {
                                originalTrustManager.checkClientTrusted(certs, authType);
                            }
                        } catch (CertificateException e) {
                            Log.w("checkClientTrusted", e.toString());
                        }
                    }

                    public void checkServerTrusted(X509Certificate[] certs, String authType) {
                        try {
                            if (certs != null && certs.length > 0){
                                certs[0].checkValidity();
                            } else {
                                originalTrustManager.checkServerTrusted(certs, authType);
                            }
                        } catch (CertificateException e) {
                            Log.w("checkServerTrusted", e.toString());
                        }
                    }
                }
        };
    }    

    private SSLSocketFactory getSSLSocketFactory()
            throws CertificateException, KeyStoreException, IOException, NoSuchAlgorithmException, KeyManagementException {
        CertificateFactory cf = CertificateFactory.getInstance("X.509");
        InputStream caInput = getResources().openRawResource(R.raw.my_cert); // this cert file stored in \app\src\main\res\raw folder path

        Certificate ca = cf.generateCertificate(caInput);
        caInput.close();

        KeyStore keyStore = KeyStore.getInstance("BKS");
        keyStore.load(null, null);
        keyStore.setCertificateEntry("ca", ca);

        String tmfAlgorithm = TrustManagerFactory.getDefaultAlgorithm();
        TrustManagerFactory tmf = TrustManagerFactory.getInstance(tmfAlgorithm);
        tmf.init(keyStore);

        TrustManager[] wrappedTrustManagers = getWrappedTrustManagers(tmf.getTrustManagers());

        SSLContext sslContext = SSLContext.getInstance("TLS");
        sslContext.init(null, wrappedTrustManagers, null);

        return sslContext.getSocketFactory();
    }
}

IMO, you should also read more at Google's Documentation - Security with HTTPS and SSL

Solution 2:

Yes, of course.

Android Volley is a library that you can use to easily and efficiently manage your networking operations over http. If the underlying layer use SSL (i.e. https) or not is totally unrelated.

In other words: the Volley framework is TCP layer agnostic and SSL only impact the TCP layer.