GERLIN61, I can understand not wanting to have voicemails from people you've blocked on your device. tikibar1, is correct that often a smartphone will route blocked numbers to a specific blocked voicemails folder or area. On an iPhone, you can quickly delete these messages in the voicemail section. When you block a number through Verizon, we don't allow the call to go through, so they can't leave a voicemail.
Outside of the free Call Blocking, there is Verizon Smart Family. As part of the many controls offered by Smart Family, you can block up to 20 numbers permanently and unknown and unlisted numbers. tikibar1's link goes over all the blocking options, here's the specific FAQ for Smart Family: https://www.verizonwireless.com/support/verizon-smart-family-faqs/
I hope you find those options beneficial.
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