Thanks for the question.
First, it is important to confirm the diagnosis of a viral wart. Callosities of the foot can also present with thickened skin on the soles and can look very much like a viral wart.
Salicylic acid can be used to treat viral warts. If the wart is persistent after 2 to 3 months of treatment or progressing in size, you can consider alternative treatments.
Cryotherapy or freezing the wart with liquid nitrogen is an alternative treatment that is commonly used to treat viral warts. Usually, a few sessions spaced weekly or fortnightly will be required.
Laser ablation of the wart is another treatment option. This can be considered if the wart is persistent or stubborn and if a single treatment without having repeated treatments is desired. Laser ablation does have a much longer downtime post treatment.
Do consider visiting your doctor or dermatologist for a proper assessment and management of the wart if this remains persistent.