Currently, most explorations about new planets are pointing to area outside Neptune's orbit, but how about inside Mercury orbit? Can we say for certain there are no planets inside Mercury's orbit?
Yes, Vulcanoids larger than 5.7 km diameter are considered to be ruled out: A Search for Vulcanoids with the STEREO Heliospheric Imager.
An object sufficiently large to be called "planet Vulcan" would change Mercury's orbit in a detectable way by gravity.
So, there are two lines of evidence, that such a planet doesn't exist.
More to read in Wikipedia: https://en.wikipedia.org/wiki/Vulcan_(hypothetical_planet)