It is widely believed that Swami Ayyappa who is the son of Shiva and Bhagavan Vishnu nullifies the effect of Shani dosham. Offering prayers to Ayyappa Swamy helps in overcoming all kinds of problems related Shani. Here is Malayalam Swami Ayyappa mantra for Shani Dosham
You should chant the mantra 108 times on all Saturdays. You can also offer prayers daily to Shasta to overcome Shani related issues in horoscope.
ഭൂതനാഥ സദാനന്ദ സർവഭൂത ദയാപര
രക്ഷരക്ഷ മഹാബാഹോ ശാസ്ത്രേ തുഭ്യം നമോനമഃ
രക്ഷരക്ഷ മഹാബാഹോ ശാസ്ത്രേ തുഭ്യം നമോനമഃ