Best investigation to diagnose H-type tracheoesophageal fistuala is:
(Refer: OP Ghai’s Essentials of Pediatrics, 8th edition, pg no: 176)

The most reliable method of establishing the diagnosis of H type fistula is by a prone tube video esophagogram. Bronchoscopy with esophagoscopy will confirm the presence of a fistula
Esophagography and/or cine esophagography, or bronchoscopy and simultaneous methylene blue administration confirmed the diagnosis of H-type TEF.
Although cine esophagography is highly effective in demonstrating H-type TEF today, bronchoscopy must be used in every patient suspected of having fistula, especially when the radiological methods fail.
X-ray
Esophagoscopy
Tracheobronchoscopy
CT scan