Shani Deva is the son of Lord Shiva through his AshtaMurty forms. AshtaMurti forms are the 8 major forms of Lord Shiva which are described in this chapter of Yajurveda Shatapatha Brahmana. The eight forms described there are:
Form of Fire, Form of Water, Form of Air, Form of Indra, Form of Plants (earth), Form of rain cloud, Form of Moon, Form of Sun.
Thus, Sun is form of Lord Shiva through his AshtaMurty form and his son is Shainaschara (Saturn). The same thing is explained also in Puranas.
Eg. 1.8 of Vishnu Purana:
एवमुक्तः पुनः सोऽथ सप्तकृत्वो रुरोद वै।
ततोऽन्यानि ददौ तस्मै सप्त नामानि वै प्रभुः।
स्थानानि चैषामष्टानां पत्नीः पुत्रांश्च वै प्रभुः।। ५ ।।
भवं सर्व महेशानं तथा पशुपति द्विज।
भीममुग्रं महादेवं उवाच स पितामहः।। ६ ।।
चक्रे नामान्यथैतानि स्थानान्येषां चकार सः।
सूर्यों जल मही वहिर्वायुराकाशमेव च।
दीक्षितो ब्राह्मणः सोम इत्येतास्तनवः क्रमात्॥७॥
सुवर्चला तथैवोमा सुकेशी चापरा शिवा।
स्वाहा दिशस्तथा दीक्षा रोहणी च यथाक्रमम् ॥८॥
सूर्यादीनां नरश्रेष्ठ रुद्राधैर्नामभिः सह।
पत्न्यः स्मृता महाभाग तदपत्यानि मे शृणु।
येषां सूतिप्रसूतैर्वा इदमापूरितं जगत् ॥ ९ ।।
शनैश्चरस्तथा शुक्रो लोहिताङ्गो मनोजवः।
स्कन्दः खर्गोऽथ सन्तानो बुधश्चानुक्रमात् सुताः॥ १०॥ (Vishnu Purana 1.8)
But, thus addressed, the boy [Rudra] still wept seven-times, and Brahma therefore gave to him seven other denominations; and to these eight persons, regions and wives and posterity belong. The eight manifestations, then, are named Rudra, Bhava, Sarva, Isana, Pasupati, Bhima, Ugra and Mahādeva, which were given to them by their great progenitor. He also assigned to them their respective stations, the Sun, water, ether, air, fire, earth, the ministrant Brahman, and the moon; for these are their several forms. The wives of the Sun and the other manifestations, termed Rudra and the rest were respectively, Suvercalā, Uma, Vikesi, Sivā, Svāhā, Dišā, Diksā and Rohiņī. Now hear an account of their progeny, by whose successive generations this world has been peopled. Their sons, then, were severally, Sanaiśocara (Saturn), Sukra (Venus), the fiery bodied Mars, Manojava, Skanda, Swarga, Santana, and Budha (Mercury).
Also in 2.13 of Linga Purana:
रुद्र इत्युच्यते देवैर्भगवान् भुक्तिमुक्तिदः ।
सूर्यात्मकस्य रुद्रस्य भक्तानां भक्तदायिनः ।।
सुवर्चला स्मृता देवी सुतश्चास्य शनैश्चरः ।
समस्तसौम्यवस्तुनां प्रकृतित्वेन विश्रुतः ।। (Linga Purana 2.13)
The Lord in the form of Sun is called Rudra by the Gods. In the form of sun he bestows prosperity to all and yields all the worldly pleasures and salvation. When he becomes Sun then his Godesses is Suvarchala and their son is Saturn (Sanaishchara).
And also in Markandeya Purana chapter 52:
(He said): - Thou, O Deva or Bright One, shall be of the name of Rudra. Do not cry. Be patient. Thus spoken to, then he cried again and again seven times. Then to him the lord gave seven other names, and also the abodes of these eight Rudras, and their wives and sons, O thou twice-born one, (were duly assigned). The lord, the Grand-father (Brahma), spoke and gave these names, - namely Bhava, Sarva, similarly Ishana, likewise Pashupati, Bhima, Ugra, Mahadeva and made abodes for these. The sun, the water, the earth, the fire, the ether, the initiated Brahman, and the moon, these became respectively their abodes. Suvarchala and similarly Uma, Vikeshi and another, Swadha, Swaha, and likewise Disha, Diksha, Rohini these respectively, O thou superior among the twice-born, became with the sun &c., the possession of the holders of the names commencing with Rudra &c.,. Their sons respectively were Shanaishchara, Shukra, Lohitanga, Monajaba, Skandha, Sarga, Santana, and Budha.
Thus ShaniDeva is the son of Lord Shiva in his AshtaMurty form. As a sidenote I discuss difference between Rudra Avatar and AshtaMurti Avatar (both take place through Brahma) in my answer here.