From Bulbapedia, the community-driven Pokémon encyclopedia.
The Professors' aides are assistants or scientists that work alongside the regional Professors. Aides specialize in many things from office work to field work.
In the games
Professor Oak's aides are scattered all over Kanto, keeping tabs on how many Pokémon the player has caught, and give out item rewards if the player has caught a sufficient amount of Pokémon. These aides usually appear on the second floor of gates or in small buildings. The rewards are usually Key Items. In addition to the stationed aides, many other aides work in Professor Oak's Laboratory, helping Professor Oak with day-to-day tasks. In total, there are three aides in the Kanto region.
There is only one aide helping out Professor Elm in the lab, and as a result of this, he and Elm are often very busy. The aide rarely goes out; when he does, it is for a very important reason. When the player enters the lab for the first time and obtains a Pokémon from Professor Elm, the aide will give the player a Potion before the player leaves. After Silver steals one of the Pokémon from the lab, he will also give the player five Poké Balls. After the player reaches Violet City and defeats Falkner, Professor Elm will send his aide off to the Violet City Pokémon Center, where he will give the player the Mystery Egg that the Professor received earlier from the player.
In FireRed and LeafGreen, the aides are very similar to those in Generation I. They still keep tabs on how many Pokémon the player has caught and give out rewards if the player have caught a sufficient amount of Pokémon. In Generation III, there is a total of five items that can be obtained from the aides.
In Generation IV, Professor Rowan's aide will always be the alternate gender player character from the player. That is, if the player chose Lucas, Dawn will be the aide, and vice versa. The aide will live in Sandgem Town with his/her little sister, grandfather, and father—who also works as an assistant of Professor Rowan. The aide is already the Professor's assistant at the beginning of the game. The aide will also demonstrates to the player how to capture Pokémon by capturing a wild Bidoof, before giving the player five Poké Balls. On Route 207, the aide will give the player a Pokétch app Dowsing Machine, and the Vs. Seeker. In Veilstone City, the aide will have their Pokédex stolen by a Galactic Grunt, but gets it back with the help of the player, as well as Looker in Platinum. The aide can be seen at different stages of the game, usually following Professor Rowan around. At the end of the game, the aide can always be found outside Professor Rowan's lab in Sandgem Town, usually giving out pieces of advice. If the player speaks to the aide when his/her birthday on the Nintendo DS calendar matches the current date, he/she will ask if it is the player's birthday.
In addition, the aforementioned aide's father will also appear in various parts of the game. He will first be seen in Route 206, giving the player an Exp. Share. He will also appear on Route 218, upgrading the Pokédex and allowing the player to view gender and form differences.
Professor Elm's aide also appears in this generation, in much the same manner as Generation II; however, rather than being in the Pokémon Center to give the player the Egg after Elm has inspected it, he is inside the Poké Mart.
In Black and White, Bianca becomes Professor Juniper's assistant after beating Alder for the first time. In Black 2 and White 2, she delivers the starter Pokémon to the player on the professor's behalf.
Dexio and Sina act as Professor Sycamore's two aides and play a pivotal role in the main plot. They are first met by the player in Route 4 describing the properties of the Fairy type, later appearing across Kalos at various points rallying out useful information, occasionally giving out Pokédex upgrades in the process. In the gate to Lumiose City, Dexio tells the player about friendship and gives the player TM27 (Return), while Sina leads you to Professor Sycamore's lab after entering the main city. During activity that involves Team Flare's nefarious schemes, the twosome appear to assist the player while disguised as the self-proclaimed defenders of Kalos beginning at the Kalos Power Plant. After the player has become Champion, the duo are seen together in the parade Professor Sycamore made for the player and their friends.
For unknown, personal reasons, Lillie is acting as an aide to Professor Kukui.
In the anime
Cosette (left) and Sophie (right), Professor Sycamore's assistants
Professors' aides, or assistants, have been prominent in the anime as well. The first ones seen were Professor Ivy's assistants Hope, Faith, and Charity. After the events of Poké Ball Peril, Brock decided to stay behind and become Ivy's assistant as well. However, in A Tent Situation, it was revealed that Brock stopped working for her under unknown circumstances.
In A Rivalry Revival, Tracey Sketchit asked Professor Oak if he could be his laboratory assistant. He agreed and has been working at the lab ever since. His job can be from either feeding the Pokémon to sweeping up around the lab.
Professor Birch has an assistant by the name of Joshua. He will often look after his laboratory when ever Birch studies outdoors.
Professor Rowan has multiple assistants at his lab, the most prominent one being Yuzo. He acted as a counselor during the Pokémon Summer Academy along with the other assistants.
Like the other Pokémon Professors, Professor Juniper also has her own set of assistants.
Professor Sycamore works with two female assistants, Sophie and Cosette. The protagonist of the Mega Evolution Specials, Alain, is a former assistant of the professor. He cut ties with him after allying with Lysandre, believing that he can protect the Professor's reputation. After the Team Flare crisis, Alain became Sycamore's assistant again.
In the manga
Blue's sister Daisy Oak served as Professor Oak's assistant starting from the Yellow chapter. Crystal took over as Professor Oak's assistant at the end of the Gold, Silver & Crystal chapter.
Professor Elm has two assistants. The first, Youngster Joey, met Gold at the start of his journey. The second, Mr. Pokémon, delivered an Egg to Gold.
Professor Rowan has two assistants. The first is Platinum's father Mr. Berlitz, who accompanied Rowan to the Canalave City academic conference. The other is Roseanne, who looked after Rowan's research lab when he was away.