## 1 Introduction  
Cognitive performance, which comprises a group of functions that includes memory, general intelligence, learning, language, orientation, perception, attention, concentration, and judgment, are regarded as important factors in a child's personal and professional attainment [1; 2]. In addition, cognition also refers to a child's ability to think and reason or to have executive function capacity, which plays a critical role in daily and social behaviors. The development of these abilities occurs throughout the childhood and adolescence periods and in parallel to developmental changes in the brain throughout the mentioned periods [3]. Attention-deficit/hyperactivity disorder (ADHD) is one of the most common neurodevelopmental disorders, with a prevalence of ~5.29% [4]. The treatment procedure is complicated and is related to the psychosocial aspects of the children [5]. Genetic and environmental factors and gut microbiota play a crucial role in developing ADHD [6; 7; 8; 9]. The pharmacological treatments for ADHD have limitations and side effects. At the same time, the efficiency of non-pharmacological treatments has not been confirmed. Cognitive capabilities and developments are influenced by many factors, including dietary factors [10]. A strong association between nutritional intake and neurocognitive development in childhood has been reported [11]. A meta-analysis disclosed that the supplementation of free fatty acids, excluding artificial food colors, improved ADHD [12; 13]. Though several factors are associated with the incidence of ADHD, gut microbiota and gut homeostasis play critical roles in it. Gut dysbiosis and altered gut homeostasis are linked to several physical and psychological complications, which affect the microbiome-gut-brain axis. Thus, the gut microbiome could be a therapeutic target for treating ADHD in children [9]. Probiotics are defined as \"live microorganisms that, when administered in adequate amounts, confer a health benefit on the host\" [14]. Probiotics are known to confer several physical and neurological health benefits in humans [15; 16; 17] and animals [18; 19]. Probiotic supplementation can improve the health-related quality of life of children and adolescents with ADHD [4]. The supplementation of probiotics positively regulates and aids in retaining a healthy microbiome in humans [16; 20]. _Lactobacillus rhamns_ GG (ATCC 53103) is a well-known probiotic that influences the host's gut microbial composition and exhibits immunomodulatory properties [21]. [PERSON] et al. [8] reported that supplementation of _L. rhamns_ GG (ATCC 53103) in early life might reduce the risk of developing neuropsychiatric disorders. Go/no-go tasks can be employed to assess the attention state of subjects with the support of electroencephalographic (EEG)/event-related potential (ERP) recordings, which enable the measurement of electrical brain activity. In the go/no-go task, participants respond to either \"go\" or \"no-go\" stimuli. The commission error rate represents the \"go\" response made by the subject on \"no-go\" trials. The response inhibition is considered better when fewer errors are made [22]. ERP supports capturing the neural activity associated with sensory and cognitive processes. ERP can be measured with the help of EEGs, a procedure that measures the brain's electrical activity over time using electrodes [23]. Tryptophan is one of the essential amino acids that supports normal growth and production and maintenance of enzymes and neurotransmitters. The metabolism of tryptophan, through the kynure pathway (KP), produces neurotoxic compounds such as quinolinic acid (QA) [24]. Serotonin is a neurotransmitter involved in several biological functions, including cognition and memory. The metabolite 5-hydroxyindoleacetic acid (5-HIAA) is one of the metabolites of serotonin. A reduction in the level of 5-HIAA directly correlates with serotonergic activity. The clinical level of 5-HIAA has been used to assess serotonergic activity.