could you tell me about arthur's bastard (and legitimate) children?
(Word of Caution: For various reasons, including inaccessibility of source materials, I am not fully read up on all the details of the source materials involving the following characters. Nor am I aware of all known children of Arthur. Therefore, I should advice discretion)
First are the two major sons, both of whom changed legitimacies as the legend evolved:
Mordred - Originally a nephew by Arthur's full sister Anna/Morgause in Historia Regum Britanniae, Mordred is later converted into Arthur's bastard son, conceived incestuously, in Vulgate Cycle. The Welsh Dream of Rhonabwy suggests that Mordred was fostered by Arthur (a normal practice of both Romans and Celts)
Loholt/Ilinot - First appeared in Erec and Enide and apparently based on the Welsh character of Llacheu, Loholt was originally a Legitimate son of Arthur by Guinevere in Perlesvaus and the German Tradition. But Vulgate Cycle alters this so that Loholt is instead another bastard son by a certain Lisanor prior to Arthur's marriage to Guinevere. In Le Morte D'Arthur, he is renamed as Borre/Bohart le Cure Hardy.
Next are the ones with Unknown Mothers (and thus of ambiguous legitimacy and relationship to Guinevere):
Amr/Amhar - Son of Arthur mentioned in Historum Brittonum as being killed by Arthur himself. His grave is described as naturally changing size with every look, implying supernatural influence. He is also mentioned in the Welsh Geraint, as one of Arthur's Four Chamberlains
Gwydre - Son of Arthur mentioned only in Culhwch and Olwen. He is killed by Twrch Trwyth alongside two maternal uncles of Arthur.
Llacheu - The most celebrated of the Welsh sons of Arthur, with mentions in Pa Gur, The Welsh Triads and other Welsh Poetic Material. Is usually identified with Loholt, with the Welsh adaptation of Perlesvaus - Y Seint Grail - being the most notable in that regard.
Duran - Son of Arthur only found in a 15th Century Welsh Manuscript, where he is said to have perished during the Battle of Camlann
Archfedd - Daughter of Arthur, found in the Welsh genealogical work Bonedd Y Saint, where she is said to have married Llawfrodedd, one of Arthur's warriors, and bore two children, Efadier and Gwrial
Apollonius, Iron and Hilde - Two sons and a daughter found in the 13th Century Icelandic Thidrekssaga.
Aristes - Son of Arthur mentioned in the Old Norse Mottuls saga
Legitimate Children of Arthur (Although not necessarily Guinevere's children)
Samson the Fair and Grega - Son and Daughter of Arthur by his wife, Queen Silvia. Both found in the Norse Samson saga fraga
Adeluf III, Morgan the Black and Patrick the Red - Three sons of Arthur, from Eldest to Youngest, from Rauf de Boun's 14th century chronicle, Petit Brut. Presumbly, sons of Queen Guinevere, but Rauf de Boun fails to mention the name of Arthur's wife. However, Adeluf III is made heir and assumes the Throne of England whilst Patrick and Morgan are given sizable inheritances in the form of Scotland and Wales. (Note: Wikipedia claims they're Arthur's sons by a fairy queen, but the cited source does not say so. Link to source HERE)
Noem - Son of Arthur and his third wife Guinevere, who died as an infant. From The History of England by Paul de Rapin de Thoyras.
Seleucia - Daughter of Arthur by his first wife, Liscanor (Lisanor), in Jorge Ferreira de Vasconcelos' 16th century Portugese novel Memorial das Proezas da Segunda Tavola Redonda. (*This technically makes her the full sister of Lisanor!Loholt) She married Arthur's successor, Sagramor Constantino (a combination of Sir Sagramore and Constantine, son of Cador) and may have even bore a daughter, Princess Licorida
Huncamunca - Daughter of Arthur and his wife, Queen Dollalolla, from Henry Fielding's 1730 Tom Thumb play
Melora - Daughter of Arthur and Guinevere from the Irish romance Eachtra Mhelóra agus Orlando. One of the more well-known daughters of Arthur and one of the very few warrior women in Arthuriana, she undergoes a world trekking adventure to gather three items needed to rescue her imprisoned beloved.
Merevie/Smerbe/Smerviemore - Son of Arthur by his second marriage to a french princess, Elizabeth. Figures primarily in the genealogical legends of Scottish Clan Campbell, who claim descent from Arthur through Smervie.
Rowland, Ellen and Two unnamed older brothers - Certain versions of the Ballad of Childe Rowland and Burd Ellen portray them as the sons and daughter of Arthur and Guinevere, apparently due to the mention of Merlin.
Locrine and Elinor - Son and Daughter of King Arthur mentioned in some ballads, such as Sir Locrine by Anna Jane Vardill.
Tryphine's son and daughter - A certain mystery play collected by François-Marie Luzel in 1863 merges Saint Tryphine from the Conomor legend with aspects of Queen Guinevere, with the primary antagonist being the lady's brother Kervoura. The two children are unnamed, but the son goes by an alias, "the Malouin"
Iduna - Daughter of Arthur and Guinevere from Edgar (1839), by Adolph Schutt
Blandine - Daughter of Arthur and Guinevere from Les Chevaliers de la Table Ronde (1937), by Jean Cocteau
Bastard Children of Arthur:
Kyduan/Cydfan - Son of Arthur by Eleich ferch Iaen. Mentioned in Culhwch and Olwen and Bonedd yr Arwyr
Arthur le Petit - Son of Arthur from Post-Vulgate, born of Arthur's deliberate rape of a daughter of Sir Tanas. Arthur le Petit serves as a "good" counterpart to Sir Mordred. He loyally serves his father incognito for many years and despises Lancelot's faction for causing the destruction of Logres. He is slain by Sir Bleoberis.
Tom a Lincoln - Eponymous hero of the 16th century romance Tom a Lincoln, by Richard Johnson. Son of Arthur by Angelica, a daughter of the Mayor of London. Fathers two additional characters, the Black Knight and the Faerie Knight.
Gyneth - Daughter of Arthur by a half-genie named Guendolen. From Walter Scott's The Bridal of Triermain (1813). A huntress whose Marriage competition results in the death of many knights including Vanoc, who is implied to be Merlin's son. As a result, Merlin puts her into an enchanted sleep for many centuries until her true love awakens her with a kiss.
And finally, those with a tenuous link to Arthuriana:
Nathalia - a supposed daughter of Arthur who accompanied St. Ursula according to De Sancta Ursula: De undecim milibus Virginum martirum (1183), by Herman Joseph
Baeddo - Wife of the Visigothic Spanish king Reccared. Claimed to be a daughter of Arthur by Compendio Historial, by Esteban de Garibay y Zamalloa
Tortolina - a daughter of Arthur according to Pantochronachanon (1652), by Thomas Urquhart
*(Additional Source link about the Daughters of King Arthur: HERE)
**This list always seeks for the latest info. Check the original post for updates.